Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.6 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.6

Inverse Function Calculator is an online tool that helps find the inverse value for the given function.

Choose the most suitable answer from the given four alternatives:

Question 1.
The value of sin-1(cos x), 0 ≤ x ≤ π is
(a) π – x
(b) x – \(\frac {π}{2}\)
(c) \(\frac {π}{2}\) – x
(d) x – π
Solution:
(c) \(\frac {π}{2}\) – x
Hint:
sin-1(cos x) = sin-1(sin(\(\frac {π}{2}\) – x)) = \(\frac {π}{2}\) – x

Question 2.
If sin-1 x + sin-1 y = \(\frac {2π}{3}\); then cos-1 x + cos-1 y is equal to
(a) \(\frac {2π}{3}\)
(b) \(\frac {π}{3}\)
(c) \(\frac {π}{6}\)
(d) π
Solution:
(b) \(\frac {π}{3}\)
Hint:
sin-1x + cos-1x + cos-1y + sin-1y = \(\frac {π}{2}\) + \(\frac {π}{2}\) = π
\(\frac {2π}{3}\) + cos-1x + cos-1y = π
cos-1x + cos-1y = π – \(\frac {2π}{3}\) = \(\frac {3π-2π}{3}\) = \(\frac {π}{3}\)

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 3.
sin-1\(\frac {3}{5}\) – cos-1\(\frac {12}{13}\) + sec-1\(\frac {5}{3}\) – cosec-1\(\frac {13}{12}\) is equal to
(a) 2π
(b) π
(c) 0
(d) tan-1\(\frac {12}{65}\)
Solution:
(c) 0
Hint:
Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6 1

Question 4.
If sin-1 x = 2sin-1 α has a solution, then
(a) |α| ≤ \(\frac {1}{√2}\)
(b) |α| ≥ \(\frac {1}{√2}\)
(c) |α| < \(\frac {1}{√2}\)
(d) |α| > \(\frac {1}{√2}\)
Solution:
(a) |α| ≤ \(\frac {1}{√2}\)
Hint:
If sin-1 x = 2sin-1 α has a solution then
–\(\frac {π}{2}\) ≤ 2sin-1α ≤ \(\frac {π}{2}\)
–\(\frac {π}{4}\) ≤ sin-1α ≤ \(\frac {π}{4}\)
sin(\(\frac {-π}{4}\)) ≤ α ≤ sin\(\frac {π}{4}\)
–\(\frac {1}{√2}\) ≤ α ≤ \(\frac {1}{√2}\)
-|α| ≤ \(\frac {1}{√2}\)

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 5.
sin-1(cos x) = \(\frac {π}{2}\) – x is valid for
(a) -π ≤ x ≤ 0
(b) 0 ≤ x ≤ π
(c) –\(\frac {π}{2}\) ≤ x ≤ \(\frac {π}{2}\)
(d) –\(\frac {π}{4}\) ≤ x ≤ \(\frac {3π}{4}\)
Solution:
(b) 0 ≤ x ≤ π
Hint:
sin-1 (cosx) = \(\frac {π}{2}\) – x is valid for
cos x = sin (\(\frac {π}{2}\) – x)
cos x ∈ [0, π]
∴ 0 ≤ x ≤ π

Question 6.
If sin-1 x + sin-1 y + sin-1 z = \(\frac {3π}{2}\), the value of show that x2017 + y2018 + z2019 – \(\frac {9}{x^{101}+y^{101}+z^{101}}\) is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:
(a) 0
Hint:
Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6 2

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 7.
If cot-1 x = \(\frac {2π}{5}\) for some x ∈ R, the value of tan-1 x is
(a) –\(\frac {π}{10}\)
(b) \(\frac {π}{5}\)
(c) \(\frac {π}{10}\)
(d) –\(\frac {π}{5}\)
Solution:
(c) \(\frac {π}{10}\)
Hint:
tan-1 x + cos-1 \(\frac {π}{2}\)
tan-1x = \(\frac {π}{2}\) – cot-1 x = \(\frac {π}{2}\) – \(\frac {2π}{5}\)
= \(\frac {5π-4π}{10}\) = \(\frac {π}{10}\)

Question 8.
The domain of the function defined by f(x) = sin-1 \(\sqrt {x-1}\) is
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) [-1, 0]
Solution:
(a) [1, 2]
Hint:
f(x) = sin-1 \(\sqrt {x-1}\)
\(\sqrt {x-1}\) ≥ 0
-1 ≤ \(\sqrt {x-1}\) ≤ 1
∴ 0 ≤ \(\sqrt {x-1}\) ≤ 1
0 ≤ x – 1 ≤ 1
1 ≤ x ≤ 2
x ∈ [1, 2]

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 9.
If x = \(\frac {1}{5}\) the value of cos(cos-1x + 2sin-1x) is
(a) –\(\sqrt{\frac {24}{25}}\)
(b) \(\sqrt{\frac {24}{25}}\)
(c) \(\frac {1}{5}\)
(d) –\(\frac {1}{5}\)
Solution:
(d) –\(\frac {1}{5}\)
Hint:
cos[cos-1x + sin-1x + sin-1x] = cos(\(\frac {π}{2}\) + sin-1x)
= -sin(sin-1x)
[∵ cos(90+θ) = -sin θ]
= -x = –\(\frac {1}{5}\)

Question 10.
tan-1(\(\frac {1}{4}\)) + tan-1(\(\frac {2}{9}\)) is equal to
(a) \(\frac {1}{2}\)cos-1(\(\frac {3}{5}\))
(b) \(\frac {1}{2}\)sins-1(\(\frac {3}{5}\))
(c) \(\frac {1}{2}\)tan-1(\(\frac {3}{5}\))
(d) tan-1(\(\frac {1}{2}\))
Solution:
(d) tan-1(\(\frac {1}{2}\))
Hint:
Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6 3

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 11.
If the function f(x) = sin-1(x² – 3), then x belongs to
(a) [-1, 1]
(b) [√2, 2]
(c) [-2, -√2]∪[√2, 2]
(d) [-2, -√2]
Solution:
(c) [-2, -√2]∪[√2, 2]
Hint:
-1 ≤ x² – 3 ≤ 1
-1 + 3 ≤ x² ≤ 1 + 3
⇒ 2 ≤ x² ≤ 4
±√2 ≤ x ≤ ± 2
[-2, -√2]∪[√2, 2]

Question 12.
If cot-1 2 and cot-1 3 are two angles of a triangle, then the third angle is
(a) \(\frac {π}{4}\)
(b) \(\frac {3π}{4}\)
(c) \(\frac {π}{6}\)
(d) \(\frac {π}{3}\)
Solution:
(b) \(\frac {3π}{4}\)
Hint:
A + B + C = π (triangle)
cot-1 2 + cot-1 3 + C = π
Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6 4

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 13.
sin-1(tan\(\frac {π}{4}\)) – sin-1(\(\sqrt{\frac {3}{x}}\)) = \(\frac {π}{6}\). Then x is root of the equation
(a) x² – x – 6 = 0
(b) x² – x – 12 = 0
(c) x² + x – 12 = 0
(d) x² + x – 6 = 0
Solution:
(b) x² – x – 12 = 0
Hint:
Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6 5

Question 14.
sin-1(2 cos²x – 1) + cos-1(1 – 2 sin²x) =
(a) \(\frac {π}{2}\)
(b) \(\frac {π}{3}\)
(c) \(\frac {π}{4}\)
(d) \(\frac {π}{6}\)
Solution:
(a) \(\frac {π}{2}\)
Hint:
sin-1(2 cos² x – 1) + cos-1(1 – 2 sin²x)
= sin-1 (2 cos² x – 1) + cos-1 (1 – sin² x – sin² x)
= sin-1(2 cos² x – 1) + cos-1(cos² x – (1 – cos²x))
= sin-1(2 cos² x – 1) + cos-1(cos² x – 1 + cos²x)
= sin-1(2 cos² x – 1) + cos-1(2 cos² x – 1)
= \(\frac {π}{2}\) [∵ sin-1 x + cos-1 x = \(\frac {π}{2}\)]

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 15.
If cot-1(\(\sqrt {sinα}\)) + tan-1(\(\sqrt {sinα}\)) = u, then cos 2u is equal to
(a) tan²α
(b) 0
(c) -1
(d) tan 2α
Solution:
(c) -1
Hint:
cot-1 x + tan-1 x = \(\frac {π}{2}\)
∴ u = \(\frac {π}{2}\)
cos 2u = cos 2(\(\frac {π}{2}\)) = cos π = -1

Question 16.
If |x| ≤ 1, then 2 tan-1 x – sin-1\(\frac {2x}{1+x²}\) is equal to
(a) tan-1x
(b) sin-1x
(c) 0
(d) π
Solution:
(c) 0
Hint:
sin-1\(\frac {2x}{1+x²}\) = 2 tan-1x
∴ 2 tan-1 x – 2 tan-1 x = 0

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 17.
The equation tan-1 x – cot-1 x = tan-1(\(\frac {1}{√3}\)) has
(a) no solution
(b) unique solution
(c) two solutions
(d) infinite number of solutions
Solution:
(b) unique solution
Hint:
tan-1 x – cot-1 x = tan-1(\(\frac {1}{√3}\)) …….. (1)
tan-1 x – cot-1 x = \(\frac {π}{2}\) ……… (2)
Add 1 and 2
2 tan-1 x = \(\frac {π}{6}\) + \(\frac {π}{2}\) = \(\frac {2π}{3}\)
tan-1 x = \(\frac {π}{3}\)
x = √3 which is uniqe solution.

Question 18.
If sin-1 x + cot-1(\(\frac {1}{2}\)) = \(\frac {π}{2}\), then x is equal to
(a) \(\frac {1}{2}\)
(b) \(\frac {1}{√5}\)
(c) \(\frac {2}{√5}\)
(d) \(\frac {√3}{2}\)
Solution:
(b) \(\frac {1}{√5}\)
Hint:
Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6 6

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Question 19.
If sin-1 \(\frac {x}{5}\) + cosec-1\(\frac {5}{4}\) = \(\frac {π}{2}\), then the value of x is
(a) 4
(b) 5
(c) 2
(d) 3
Solution:
(d) 3
Hint:
Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6 7

Question 20.
sin(tan-1 x), |x| < 1 is equal to
(a) \(\frac {x}{\sqrt{1-x^2}}\)
(b) \(\frac {1}{\sqrt{1-x^2}}\)
(c) \(\frac {1}{\sqrt{1+x^2}}\)
(d) \(\frac {x}{\sqrt{1+x^2}}\)
Solution:
(d) \(\frac {x}{\sqrt{1+x^2}}\)
Hint:
tan a = x
W.K.T 1 + tan² a = sec² a
1 + x² = sec² a
sec a = \(\sqrt{1+x^2}\)
\(\frac {1}{cosa}\) = \(\sqrt{1+x^2}\)
cos a= \(\frac {1}{\sqrt{1+x^2}}\)
sin a = \(\sqrt{1-cos^2a}\) = \(\sqrt{1-\frac {1}{1+x^2}}\)
\(\sqrt{\frac{1+x^2 -1}{1+x^2}}\) = \(\frac {x}{\sqrt{1+x^2}}\)

Samacheer Kalvi 12th Maths Guide Chapter 4 Inverse Trigonometric Functions Ex 4.6

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Accountancy Guide Pdf Chapter 9 Rectification of Errors Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Accountancy Solutions Chapter 9 Rectification of Errors

11th Accountancy Guide Bank Rectification of Errors Text Book Back Questions and Answers

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

I. Multiple Choice Questions

Choose the correct answer.

Question 1.
Error of principle arises when ________.
a) There is complete omission of a transaction
b) There is partial omission of a transaction
c) Distinction is not made between capital and revenue items
d) There are wrong postings and wrong castings
Answer:
c) Distinction is not made between capital and revenue items

Question 2.
Errors not affecting the agreement of trial balance are ________.
a) Errors of principle
b) Errors of overcasting
c) Errors of undercasting
d) Errors of partial omission
Answer:
a) Errors of principle

Question 3.
The difference in trial balance is taken to ________.
a) The capital account
b) The trading account
c) The suspense account
d) The profit and loss account
Answer:
c) The suspense account

Question 4.
A transaction not recorded at all is known as an error of ________.
a) Principle
b) Complete omission
c) Partial omission
d) Duplication
Answer:
b) Complete omission

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 5.
Wages paid for installation of machinery wrongly debited to wages account is ah error of ________.
a) Partial omission
b) Principle
c) Complete omission
d) Duplication
Answer:
b) Principle

Question 6.
Which of the following errors will not affect the trial balance?
a) Wrong balancing of an account
b) Posting an amount in the wrong account but on the correct side
c) Wrong totaling of an account
d) Carried forward wrong amount in a ledger account
Answer:
b) Posting an amount in the wrong account but on the correct side

Question 7.
Goods returned by Senguttuvan were taken into stock, but no entry was passed in the books. While rectifying this error, which of the following accounts should be debited?
a) Senguttuvan account
b) Sales returns account
c) Returns outward account
d) Purchases returns account
Answer:
b) Sales returns account

Question 8.
A credit purchase of furniture from Athiyaman was debited tg purchases account. Which of the following accounts should be debited while rectifying this error?
a) Purchases account
b) Athiyaman account
c) Furniture account
d) None of these
Answer:
c) Furniture account

Question 9.
The total of purchases book was overcast. Which of the following accounts should be debited in the rectifying journal entry?
a) Purchases account
b) Suspense account
c) Creditor account
d) None of the above
Answer:
b) Suspense account

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 10.
Which of the following errors will be rectified using suspense account?
a) Purchases returns book was undercast by ₹ 100
b) Goods returned by Narendran was not recorded in the books ;
c) Goods returned by Akila ₹ 900 was recorded in the sales returns book as ₹ 90
d) A credit sale of goods to Ravivarman was not entered in the sales book.
Answer:
a) Purchases returns book was undercast by ₹ 100

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

II. Very Short Answer Type Questions

Question 1.
What is meant by the rectification of errors?
Answer:
Correction of errors in the books of accounts is not done by erasing, rewriting, or striking the figures which are incorrect. Correcting the errors that have occured is called Rectification.

Question 2.
What is meant by the error of principle?
Answer:
The error of principle means the mistake committed in the application of fundamental accounting principles in recording a transaction in the books of accounts.

Question 3.
What is meant by the error of partial omission?
Answer:
When the accountant has failed to record a part of the transaction, it is known as an error of partial omission. This error usually occurs in posting. This error affects only one account.

Question 4.
What is meant by the error of complete omission?
Answer:
It means the failure to record a transaction in the journal or subsidiary book or failure to post both the aspects in the ledger. This error’ affects two or more accounts.

Question 5.
What are compensating errors?
Answer:
The errors that make up for each other or neutralize each other are known as compensating errors. These errors may occur in related or unrelated accounts. Thus, excess debit or credit in one account may be compensated by excess credit or debit in some other account. These are also known as offsetting errors.

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

III. Short Answer Questions

Question 1.
Write a note on the error of principle by giving an example.
Answer:
It means the mistake committed in the application of fundamental accounting principles in recording a transaction in the books of accounts.
Example:
Entering the purchase of an asset in the purchases book. Machinery purchased on credit for ₹ 10,000 by M/s. Anbarasi garments manufacturing company entered in the purchases book.

Question 2.
Write a note on the suspense account.
Answer:
1. When the trial balance does not tally, the amount of difference is placed to the debit (when the total of the credit column is higher than the debit column) or credit (when the total of the debit column is higher than the credit column) to a temporary account known as ‘suspense account

2. Suspense account will remain in the books until the location and rectification of errors.

3. Afterrectifying the errors and posting the rectification entries to the respective ledger accounts, the suspense account appearing in the ledger is to be balanced.

4. If all the errors are located and rectified, the suspense account gets closed.

Question 3.
What are the errors not disclosed by a trial balance?
Answer:
Certain errors will not affect the agreement of trial balance. Though such errors occur in the books of accounts, the total debit and credit balance will be the same. The trial balance will tally. Errors of complete omission, error of principle, compensating error, a wrong entry in the subsidiary books are not disclosed by the trial balance.

Question 4.
What are the errors disclosed by a trial balance?
Answer:
Certain errors affect the agreement of trial balance. If such errors have occurred in the books of accounts, the total of debit and credit balances will not be the same. The trial balance will not tally. The error of partial omission and error of commission affect the agreement of trial balance.
Examples of such errors are as follows:

  • Entered in the journal but posted to one account and omitted to be posted to the other.
  • Posting an amount to the wrong side of a ledger account
  • Posting twice in a ledger account.
  • Over-casting or under-casting in a subsidiary book.
  • Posting a wrong amount to the wrong side of an amount.
  • Errors in carrying forward the page total from one page to the next page of an account or subsidiary book.
  • Errors arising in the balancing of an account.
  • Omission to post an entry from a subsidiary book.

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 5.
Write a note on one-sided errors and two-sided errors.
Answer:
(a) Rectification of one-sided errors before preparing trial balance:

  • When a one-sided error is detected before preparing the trial balance, no journal entry is required to be passed in the books.
  • In such cases, the error can be rectified by giving an explanatory note in the account affected as to whether the concerned account is to be debited or credited.
  • Example: Sales book is undercast by ₹ 100.
  • In this case, the sales book is undercast by ₹ 100.
  • The total of sales book is posted to the credit side of the sales account in the ledger.
  • The under casting has resulted in an under-crediting of sales accounts by ₹ 100.
  • This is an error of commission.
  • The error is only in the sales account. There is short credit in the sales account by ₹ 100. Hence, it is rectified by crediting sales account by ₹ 100.

(b) Rectification of two-sided errors before preparing the trial balance:
1. When a two-sided error is detected before preparing the trial balance, it must be rectified by passing a rectifying journal entry in the journal proper after analyzing the error.
Example: Goods sold to Anand for ₹ 1,000 on credit was not entered in the sales book. The entry will be
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 1
Method of deriving the rectifying entries
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 2

IV. Exercises

Question 1.
State the account/s affected in each of the following errors
a) Goods purchased on credit from Saranya for ₹ 150 was posted to the debit side of her account.
b) The total of purchases book ₹ 4,500 was posted twice.
Solution:
a) Saranya account should be credit with ₹ 300
b) Purchases account should be credit with ₹ 4,500

Question 2.
State the account/s affected in each of the following errors
a) Goods sold to Vasu on credit for ₹ 1,000 was not recorded in the sales book.
b) The total of the sales book ₹ 2,500 was posted twice.
Solution:
a) Sales account should be credit with ₹ 1,000
b) Sales account should be Debited with ₹ 2,500

Question 3.
Rectify the following errors discovered before the preparation of the trial balance
a) Sales book was undercast by ₹ 100
b) Purchases returns book was overcast by ₹ 200
Solution:
a) Sales account should be Credited with ₹ 100
b) Purchases returns account should be debited with ₹ 200

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 4.
Rectify the following errors before the preparation of trial balance
a) Returns outward book was undercast by ₹ 2,000
b) Returns inward book total was taken as ₹ 15,000 instead of ₹ 14,000
c) The total of the purchases account was carried forward ₹ 100 less.
Solution:
a) Purchases return account should be Credited with ₹ 2,000
b) Sales returns account should be Debited with ₹ 1,000
c) Purchases accounts should be debited ₹ 100

Question 5.
Rectify the following errors assuming that the trial balance is yet to be prepared
a) Sales book was undercast by ₹ 400
b) Sales returns book was overcast by ₹ 500
c) Purchases book was undercast by ₹ 600
d) Purchases returns book was overcast by ₹ 700
e) Bills receivable book was undercast by ₹ 800
Solution:
a) Sales account should be credited with ₹ 400
b) Sales return accounts should be Credited with ₹ 500
c) Purchases account should be debited with ₹ 600
d) Purchases returns account should be debited with ₹ 700
e) Bills received account should be debited with ₹ 800

Question 6.
Rectify the following errors before preparing trial balance
a) The total of purchases book was carried forward ₹ 90 less.
b) The total of purchases book was carried forward ₹ 180 more.
c) The total of sales book was carried forward ₹ 270 less.
d) The total of sales returns book was carried forward ₹ 360 more.
e) The total of purchase returns book was carried forward ₹ 450 less.
Solution:
a) Purchases account is to be Debited with ₹ 90
b) Purchases account is to be Credited with ₹ 180
c) Sales account is to be Credited with ₹ 270
d) Sales returns account is to be Credited with ₹ 360
e) Purchases returns account is to be Credit with ₹ 450

Question 7.
The following errors were located by the accountant before the preparation of trial balance. Rectify them.
a) The total of the discount column of ₹ 1,100 on the debit side of the cash book was not yet osted.
b) The total of the discount column on the credit side of the cash book was undercast by ₹ 500.
c) Purchased goods from Anbuchelvan on credit for ₹ 700 was posted to the debit side of his account.
d) Sale of goods to Ponmukil on credit for ₹ 78 was posted to her account as ₹ 87.
e) The total sales returns book of ₹ 550 was posted twice.
Solution:
a) Discount account should be debited with ₹ 1,100
b) Discount account should be Credited with ₹ 500
c) Anbuchelvan account should be Credited with ₹ 1,400
d) Ponmuki account should be Credit with ₹ 9
e) Sales return account should be Credit with ₹ 550

Question 8.
The accountant of a firm located the following errors before preparing the trial balance. Rectify them.
a) Machinery purchased for ₹ 3,000 was debited to the purchases account.
b) Interest received ₹ 200 was credited to the commission account.
c) An amount of ₹ 1,000 paid to Tamil selvan as salary was debited to his personal account.
d) Old furniture sold for ₹ 300 was credited to sales account.
e) Goods worth ₹ 800 purchased from Soundarapandian on credit was not recorded in the books of accounts.
Solution:
Journal Entries
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 3

Question 9.
Rectify the following errors which were located before preparing the trial balance.
a) Wages paid ₹ 2,000 for the erection of machinery was debited to wages account.
b) Sales returns book was short totaled by ₹ 1,000.
c) Goods purchased for ₹ 200 were posted as ₹ 2,000 to the purchases account.
d) The sales book was overcast by ₹ 1,500.
e) Cash paid to Mukil ₹ 2,800 which was debited to Akhil’s account as ₹ 2,000.
Solution:
Rectification of Errors:
 Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 5

Question 10.
Rectify the following errors which were located at the time of preparing the trial balance
a) The total of the discount column on the debit side of the cash book of ₹ 225 was posted twice.
b) Goods of the value of ₹ 75 returned by Ponnarasan were not posted to his account.
c) Cash received from Yazhini ₹ 1,000 was not posted.
d) Interest received ₹ 300 has not been posted.
e) Rent paid ₹ 100 was posted to rent account as ₹ 10
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 6

Question 11.
The following errors were located at the time of preparing the trial balance. Rectify them.
a) A personal expense of the proprietor ₹ 200 was debited to the traveling expenses account.
b) Goods of ₹ 400 purchased from Ramesh on credit was wrongly credited to Ganesh’s account.
c) An amount of ₹ 500 paid as salaries to Mathi was debited to his personal account.
d) An amount of ₹ 2,700 paid for the extension of the building was debited to the repairs account.
e) A credit sale of goods of ₹ 700 on credit to Mekala was posted to Krishnan’s account.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 7

Question 12.
Rectify the following journal entries.
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 8
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 9

Question 13.
Rectify the following errors discovered after the preparation of the trial balance
a) Rent paid was carried forward to the next page ₹ 500 short.
b) Wages paid were carried forward ₹ 250 excess.
Solution:
a) Rent account should be debited with ₹ 500
b) Wages account should be Credited with ₹ 250

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 14.
Rectify the following errors after preparation of trial balance
a) Salary paid to Ram ₹ 1,000 was wrongly debited to his personal account.
b) A credit sale of goods to Balu for ₹ 450 was debited to Balan.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 10

Question 15.
Pass necessary journal entries to rectify the following errors located after the preparation of trial balance
a) Sales book was undercast by ₹ 1,000.
b) A amount of ₹ 500 paid for wages was wrongly posted to the machinery Account.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 11

Question 16.
Give journal entries to rectify the following errors discovered after the preparation of trial balance
a) Purchases book was overcast by ₹ 10,000.
b) Repairs to the furniture of ₹ 500 were debited to the furniture account.
c) A credit sale of goods to Akilnilavan for ₹ 456 was credited to his account as ₹ 654.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 12

Question 17.
Rectify the following errors located after the preparation of trial balance
a) Purchases book was undercast by ₹ 900.
b) Sale of old furniture for ₹ 1,000 was credited to sales account.
c) Purchase of goods from Arul for ₹ 1,500 on credit was not recorded in the books.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 13

Question 18.
The following errors were located after the preparation of the trial balance. Pass journal entries to rectify them. Assume that there exists a suspense account.
a) The total sales book was undercast by ₹ 350.
b) The total of the discount column on the debit side of the cash book ₹ 420 was not posted.
c) The total of one page of the purchases book of ₹ 5,353 was carried forward to the next page as ₹ 5,533.
d) Salaries ₹ 2,400 were posted as ₹ 24,000.
e) Purchase of goods from Sembiyanmadevi on credit for ₹ 180 was posted to her account as ₹ 1,800
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 14

Question 19.
Rectify the following errors assuming that the trial balance is already prepared and the difference was placed to suspense account
a) Sales book was undercast by ₹ 250
b) Purchases book was undercast by ₹ 120
c) Sales book was overcast by ₹ 130
d) Bills receivable book was undercast by ₹ 75
e) Purchases book was overcast by ₹ 35.’
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 15

Question 20.
The following errors were located after the preparation of the trial balance. The difference in trial balance has been taken to the suspense account. Rectify them.
a) The total of purchases book was carried forward ₹ 70 less.
b) The total sales book was carried forward ₹ 340 more.
c) The total of purchases book was carried forward ₹ 150 more.
d) The total of sales book was carried forward ₹ 200 less.
e) The total of purchase returns book was carried forward ₹ 350 less.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 16

Question 21.
The following errors were located by the accountant after the preparation of the trial balance. There exists a suspense account. Rectify them.
a) The total of the discount column of ₹ 1,180 on the debit side of the cash book was not posted.
b) Purchase of goods from Arivuchelvan on credit for ₹ 600 was posted to the debit side of his account.
c) The total of the discount column on the credit side of the cash book was undercast by ₹ 400.
d) The total sales returns book of ₹ 570 was posted twice.
e) Sold goods to Mukil on credit for ₹ 87 was posted to her account as ₹ 78.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 17

Question 22.
The accountant of a firm located the following errors after preparing the trial balance. Rectify them assuming that there is a suspense account.
a) Machinery purchased for ₹ 3,500 was debited to purchases account.
b) ₹ 1,800 paid to Raina as salary was debited to his personal account.
c) Interest received ₹ 200 was credited to the commission account.
d) Goods worth ₹ 1,800 purchased from Amudhanila on credit was not recorded in the books of accounts,
e) Used furniture sold for ₹ 350 was credited to the sales account.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 18

Question 23.
The book-keeper of a firm found that the trial balance was cut by ₹ 922 (excess credit). He placed the amount in the suspense account and subsequently found the following errors
a) The total discount column on the credit side of the cash book ₹ 78 was not posted in the ledger.
b) The total of purchases book was short by ₹ 1,000.
c) A credit sale of goods to Natarajan for ₹ 375 was entered in the sales book as ₹ 735.
d) A credit sale of goods to Mekala for ₹ 700 was entered in the purchases book.
You are required to give rectification entries and prepare a suspense account.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 19
Suspense Account
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 20

Question 24.
The books of Raman did not agree. The accountant placed the difference of ₹ 1,270 to the debit of the suspense account. Rectify the following errors and prepare the suspense account
a) Goods taken by the proprietor for his personal use ₹ 75 was not entered in the books.
b) A credit sale of goods to Shanmugam for ₹ 430 was credited to his account as ₹ 340.
c) A purchase of goods on credit for ₹ 400 from Vivek was entered in the sales book. However, Vivek’s account was correctly credited.
d) The total of the purchases returns book ₹ 300 was not posted.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 21
Suspense Account
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 22

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

11th Accountancy Guide Rectification of Errors Additional Important Questions and Answers

I. Choose the correct answer.

Question 1.
The errors can be classified into ……………… types.
(a) One
(b) Two
(c) Three
(d) Four
Answer:
(d) Four

Question 2.
When one or both aspects of a transaction are recorded in the wrong category of an account, this is called ________.
a) Error of Principle
b) Error of Omission
c) Error of Commission
d) Error of original entry
Answer:
a) Error of Principle

Question 3.
The errors that make up for each other or neutralize each other are known as ………………
(a) Errors of commission
(b) Errors of principle
(c) Errors of omission
(d) Compensating errors
Answer:
(d) Compensating errors

Question 4.
₹ 60,000 paid on the extension of the building wrongly debited to Repairs account. This is called the error of ________.
a) Commission
b) Omission
c) Principle
d) None of these
Answer:
c) Principle

Question 5.
Sales book is undercast by ₹ 100, classify the error
(a) Errors of principle
(b) Errors of commission
(c) Errors in casting
(d) Errors of omission
Answer:
(c) Errors in casting

Question 6.
________ are those which cancel themselves out.
a) Error of principle
b) Error of Commission
c) Error of Omission
d) Compensating errors
Answer:
d) Compensating errors

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 7.
________ errors can be located in the preparation of trial balance.
a) Error of principle
b) Error of Commission
c) Error of Omission
d) Compensating errors
Answer:
b) Error of Commission

Question 8.
An entry of ₹ 75 has been debited to Rajesh’s A/c as ₹ 57 is an error of ________.
a) Error of principle
b) Error of Commission
c) Error of Omission
d) Compensating errors
Answer:
b) Error of Commission

Question 9.
Casting errors are the result of ________.
a) Wrong totaling
b) Wrong Balancing
c) the wrong carry forward
d) None of the above
Answer:
a) Wrong totaling

Question 10.
Suspense account is usually closed when ________.
a) Accounts are finalized
b) After the completion of auditing
c) All the errors are rectified
d) None of the above
Answer:
c) All the errors are rectified

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

II. Very Short Answer Questions

Question 1.
What is error or omission?
Answer:
The failure of the accountant to record a transaction or an item in the books of accounts is known as an error of omission. It can be a complete omission or partial omission.

Question 2.
At what stages the errors can occur?
The following types of errors may occur in various stages:
Answer:

  • At the stage of journalizing
  • At the stage of posting
  • At the stage of balancing
  • At the stage of preparing trial balance

Question 3.
What do you mean by errors?
Answer:
Errors mean recording or classifying or summarising the accounting transactions wrongly or omissions to record them by a clerk or an accountant unintentionally.

Question 4.
What is an error or omission?
Answer:
The failure of the accountant to record a transaction or an item in the books of accounts is known as an error of omission. It can be a complete omission or partial omission.

Question 5.
What is an error of commission?
Answer:
When a transaction is incorrectly recorded, it is known as error of commission. It usually occurs due to lack of concentration or carelessness of the accountant.

Question 6.
Write a note on one-sided errors.
Answer:
When a one-sided error is detected before preparing the trial balance, no journal entry is required to be passed in the books. In such cases, the error can be rectified by giving an explanatory note in the account affected as to whether the concerned account is to be debited or credited.

Question 7.
Write a note on two-sided errors.
Answer:
When a two-sided error is detected before preparing the trial balance, it must be rectified by passing a rectifying journal entry in the journal proper after analyzing the error.

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

III. Short Answer Questions

Question 1.
What are the steps to be followed to locate the errors after the preparation of the trial balance?
Answer:
While preparing trial balance, if it does not tally, it is an indication of the presence of errors in the books of accounts. The difference in the trial balance is transferred to the suspense account and then errors are to be located and rectified.

The following are the steps to be followed to locate errors after preparing a trial balance

  1. The totals of debit and credit columns of trial balance are to be checked
  2. The balances of various ledger accounts shown in the trial balance are to be checked to ensure whether they are shown in the respective columns (debit or credit).
  3. The difference in the trial balance must be halved and compared with the balances of the ledger to verify whether any ledger balance is recorded on the wrong side of the trial balance.
  4. The totals of all the subsidiary books are to be checked, especially if the difference is ₹ 1, ₹ 100, etc.
  5. If the difference is divisible by ‘9’, the difference may be due to the transposition of figures in the books (Writing ₹ 127 as ₹ 172). Hence, the possibilities of transposition of figures shall be checked.
  6. The accounts of all the creditors and debtors are to be verified.
  7. The correctness of the balances of various ledger accounts is to be ensured.
  8. The correctness of the balances of various ledger accounts is to be ensured.
  9. All the amounts carried forward from one page to the next are to be verified. .
  10. If the difference still exists, as a final step all the entries in the journals should be verified.

Question 2.
What are the steps to be followed to locate the errors before preparation of trial balance?
Answer:
Errors may be located before preparing the trial balance either spontaneously or by intentional scrutiny of books of accounts.

The following are the steps to be followed to locate errors before preparing trial balance:

  1. Scrutiny of entries made in the journal proper
  2. Scrutiny of entries made in the subsidiary books
  3. Checking the totals of the subsidiary books
  4. Scrutiny of postings made to the ledger accounts
  5. Scrutiny of balancing of ledger accounts

Question 3.
Spot out the location of errors before preparation of trial balance.
Answer:
Errors may be located before preparing the trial balance either spontaneously or by intentional scrutiny of books of accounts. The following are the steps to be followed to locate errors before preparing trial balance

  1. Scrutiny of entries made in the journal proper.
  2. Scrutiny of entries made in the subsidiary books.
  3. Checking the totals of the subsidiary books
  4. Scrutiny of balancing of ledger accounts.
  5. Scrutiny of postings made to the ledger accounts

Question 4.
Rectify the following errors

  1. Purchases Book is overcast by ₹ 3,500
  2. Sales Book is undercast by ₹ 2,000
  3. Purchases returns books have been overcast by ₹ 7,600
  4. Sales returns book has been undercast by ₹ 500

Solution:
Rectification:

  1. Credit Purchases Account with ₹ 3,500
  2. Credit Sales Account with ₹ 2,000
  3. Debit Purchases Returns account with ₹ 7,600
  4. Debit Sales returns account with ₹ 500

Question 5.
Rectify the following errors
1. Sales book undercast by ₹ 5,000
2. Machinery purchased for ₹ 9000 passed through purchases Book.
3. Sales to Ram for ₹ 11,000 debited to his account as ₹ 10,100.
4. Repairs to building ₹ 3,640 debited to buildings account.
Solution:
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 23

Question 6.
Rectify the following errors
1. The purchase of machinery from A for ₹ 3,000 has been entered in the purchase daybook.
2. Received ₹ 1,000 from M but credited to N’s account.
3. ₹ 800 paid as wages for the erection of machine has been charged to Repairs account.
4. ₹ 250 received from Ganesh, previously written off, has been credited to Ganesh account
Solution:
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 23a

Question 7.
Rectify the following Errors
1. Purchase book is overcast by ₹ 6,000
2. Sales book carried forward ₹ 630 instead of ₹ 360
3. Purchase from Sreesha ₹ 5, 000 has been posted to the debit side of her account.
4. Sale of old machinery for ₹ 50,000 has been entered in Sales book.
Solution:
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 24

Question 8.
Rectify the following error
1. Salary paid to manager ₹ 8,000 debited to his personal account.
2. Total the discount column in the debit side of the cash book is wrongly cast short. ₹ 540.
3. Total of sales book has been added ₹ 2,400 excess
4. ₹ 230 received in respect of a book debt was posted to the sales account
5. Goods sold for ₹ 3,873 to Raju were returned to us and recorded in the sales book.
Solution:
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 25

Question 9.
When a Trial Balance failed to agree, ₹ 37,900 was transferred to the credit of the suspense account. The following errors were discovered. Give journal entries and prepare a suspense account.
1. Sales daybook was undercast by ₹ 40,000
2. Purchase of machinery for ₹ 60,000 was passed through the purchase book.
3. Goods sold to Velu for ₹ 4,500 were posted to his account as ₹ 5,400.
4. Purchase returns book was overcast by ₹ 2,000
5. The total sales book from one page was carried forward to the next page as ₹ 12,000 instead of ₹ 11,000.
Solution:
Rectification of Entries
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 26
Suspense Account
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 27

Question 10.
In considering the trial balance, a book-keeper finds that the debit total exceeds the credit total by ₹ 3,520. The amount is placed to the credit of a newly opened suspense account. The following mistakes were discovered. Pass the necessary entries for rectifying the mistakes and show the suspense account.
a) Sales daybook was overcast by ₹ 1000
b) A sale of ₹ 500 to Rajesh was wrongly debited to Ramesh
c) General expenses ₹ 180 was posted as ₹ 800.
d) Cash received from Ganesh was debited to his account ₹ 1,500
e) While carrying forward the total of one page of the purchases day book to the next the amount of ₹ 12,350 was entered as ₹ 13,250.
Solution:
Rectification of Entries
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 26
Suspense Account
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 27

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 11.
Pass journal entries to rectify the following entries
1. ₹ 4,500 received in respect of a book debt was posted to sales account
2. Defective goods worth ₹ 260 returned to Saran were recorded through the sales returns book.
3. Goods sold for ₹ 950 to Rakesh were returned to us and recorded in the sales book.
4. A purchase of ₹ 2,100 from Banu on the last day of the year was taken into stock, but the invoice was not passed through the purchase book.
Solution:
Rectification of Entries
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 28

Question 12.
Show how you will rectify the following entries.
1. A Credit sales of ₹ 650 to Raja were debited to Kaja.
2. A purchase of goods for ₹ 750 from Shaji was debited to his account.
3. An office typewriter purchased for ₹ 6,500 was debited to the Repairs account.
4. A sum of ₹ 3,900 received from a debtor was debited to his account.
5. Purchase of goods for the consumption of proprietor was debited to purchase account ₹ 1,000
Solution:
Rectification of Entries
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 28a

Question 13.
Write down the rectifying journal entries for the following errors and show the suspense account.
1. The sales returns books have been undercast by ₹ 5,000
2. Goods worth ₹ 1,500 sold to Batiya have been credited to his account.
3. Purchase of furniture ₹ 7,000 has been entered in the purchases account.
4. Cash Rs.4,500 from Aadhira has been posted to his account as ₹ 5,400.
5. A bill received from X for ₹ 4,000 has been posted to the Bills payable account.
Solution:
Rectification of Entries
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 28
Suspense Account
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 29

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

IV. Long Question Answers

Question 1.
Explain the steps to be followed to locate errors after preparing a trial balance
Answer:
The following steps are to be followed to locate errors after preparing a trial balance

  1. The totals of the debit and credit columns of the trial balance are to be checked.
  2. The balances of various ledger accounts shown in the trial balance are to be checked to ensure whether they are shown in the respective columns (debit or credit).
  3. The difference in the trial balance must be halved and compared with the balances of the ledger to verify whether any ledger balance is recorded on the wrong side of the trial balance.
  4. The totals of all the subsidiary books are to be checked, especially if the difference is ₹1 to ₹ 100 etc.
  5. If the difference is divisible by 9 the difference may be due to the transposition of figures in the books. (Writing ₹ 127 as ₹ 172). Hence, the possibilities of transposition of figures shall be checked.
  6. The accounts of all the creditors and debtors are to be verified.
  7. Postings from the subsidiary books to different accounts in the ledger are to be checked.
  8. The correctness of the balances of various ledger accounts is to be ensured.
  9. All the amounts carried forward from one page to the next area to be verified.
  10. If the differences still exists, as a final step all the entries in the journals should be verified.

Question 2.
Briefly explain the Classification or errors
Answer:
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 30
The failure of the accountant to record a transaction or an item in the books of accounts is known as an error of omission. It can be a complete omission or partial omission.
1. Error of complete omission – It means the failure to record a transaction in the journal or subsidiary book or failure to post both the aspects in the ledger. This error affects two or more accounts.

2. Error of partial omission – When the accountant has failed to record a part of the transaction, it is known as an error of partial omission. This error usually occurs in posting. This error affects only one account.

3. Error of commission – When a transaction is incorrectly recorded, it is known as an error of commission. It usually occurs due to lack of concentration or carelessness of the accountant.

Errors of Principle: It means the mistake committed in the application of fundamental accounting principles in recording a transaction in the books of accounts.

4. Compensating errors – The errors that make up for each other or neutralize each other are known as compensating errors. These errors may occur in related or unrelated accounts. Thus, excess debit or credit in one account may be compensated by excess credit or debit in some other account. These are also known as offsetting errors.

5. Errors disclosed by the trial balance and errors not disclosed by the trial balance – Generally, one-sided errors are revealed by a trial balance. They will cause disagreement of totals of debit balances and credit balances. Two-sided errors are not revealed by a trial balance.

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

V. Additional Sums

Question 1.
Rectify the following errors
i) Purchases book overcast by ₹ 1,300
ii) Sales book under cast by ₹ 2,500
Solution:
i) Credit – Purchases A/c with ₹ 1,300
ii) Credit – Sales A/c with ₹ 2,500

Question 2.
Rectify the following errors
i) Purchases return book overcast by ₹ 750
ii) Sales return book under cast by ₹ 600
Solution:
i) Debit – Purchases return A/c with ₹ 750
ii) Debit – Sales return A/c with ₹ 600

Question 3.
Rectify the following errors
i) Purchases book is carried forward ₹ 850 Less
ii) Sales book total is carried toward ₹ 2,500 More
Solution:
i) Debit – Purchases A/c with ₹ 850
ii) Debit – Sales A/c with ₹ 2,500

Question 4.
Rectify the following errors
i) A total of ₹ 7,580 in the purchases book has been carried forward as ₹ 8,570
ii) The total of the sales book ₹ 7,500 or page 20 was carried forward to page 21 as ₹ 5,570
iii) Purchases return book was carried forward as ₹ 1,520 instead of ₹ 5,120
Solution:
i) Credit – Purchases A/c with ₹ 990
ii) Credit – Sales A/c with ₹ 1,980
iii) Credit – Purchases return A/c with ₹ 3,600

Question 5.
Rectify the following errors
i) Purchases from Bagavathi for ₹ 4,500 has been posted to the debit side of her account
ii) Sales to Vijay for ₹ 1,520 has been posted to his credit as ₹ 1,250
Solution:
i) Purchases from Bagavathi should have been posted to the credit of Bagavathi’s A/c, but it has been . debited. Hence, credit Bagavathi’s A/c with double the amount i.e, ₹ 9,000

ii) Sales to Vijay has to be debited in Vijay’s account but his account is credited with ₹ 1,250. Hence Debit Vijay’s A/c with ₹ 1,250 to ₹ 1,520 i.e, ₹ 2,770

Question 6.
Rectify the following errors
i) Purchases from should for ₹ 750 has been omitted to be posted to the personal A/c
ii) Sales to Khader for ₹ 780 has been posted to his account as ₹ 870
Solution:
i) This is an error of omission. Posting must be to the credit of Shakila’s A/c. Hence, post ₹ 750 to the credit of Skakila’s A/c.

ii) Here Khader’s has been debited with a wrong amount i.e., with an excess amount. To rectify this error, the excess amount must be credited to his account. Hence, Credit Khader’s A/c with ₹ 90.

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 7.
The following errors were found in the book of pradhu. Give the necessary entries to correct them.
i) Salary of ₹ 10,000 paid to Murali has been debited to his personal account.
ii) ₹ 3,500 paid for a typewriter was charged to the office expenses account.
iii) ₹ 8,000 paid for furniture purchased has been charged to the purchases account.
iv) Repairs made were debited to the building account for ₹ 500
v) An amount of ₹ 5,000 withdrawn by the proprietor for his personal use has been debited to the trade expenses account.
iv) ₹ 2,000 received from Shanthi and Co. has been wrongly entered as from Shakila and Co.
Solution:
In the book of Prathu – Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 31

Question 8.
Give journal entries to rectify the following errors
i) Purchases of goods from Devi amounting to ₹ 25,000 have been wrongly passed through the sales Book.
ii) Credit sale of goods ₹ 30,000 to Rajan has been wrongly passed through the purchases Book
iii) Sold old furniture for ₹ 3,500 passed through the sales Book.
iv) Paid wages for the construction of Building debited to wages to account ₹ 1,00,000
v) Paid ₹ 10,000 for the installation of machinery debited to wages account.
vi) On 31st December 2003 goods worth ₹ 5,000 were returned by Manjia and were taken into stock on the same date, but no entry was passed in the books.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 32

Question 9.
An accountant could not tally the Trial Balance. The difference of ₹ 5,180 was Temporality placed to the credit of suspense account for preparing the final account. The following errors were taken located.
i) Commission of ₹ 500 paid, was posted twice, once to, discount allowed account and once to commission account.
ii) The sales book was undercast by ₹ 1,000
iii) A Credit sales of ₹ 2,780 to Raja though correctly entered in the sale book, was posted wrongly to her account as Rs.3,860
iv) A Credit purchase from Nataraj of ₹ 1,500, though correctly entered in the purchases book, was wrongly debited to his personal account.
v) Discount column of the payments side of the book was wrongly added as ₹ 2,800 instead of ₹ 2,400
You are required to
i) Pass the necessary rectifying entries.
ii) Prepare suspense Account.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 33
Suspense Account
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 34

Question 10.
Rectify the following Journal Entries
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 35
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 36

Question 11.
Rectify the following Errors
i) ₹ 12,000 paid of salary to cashier Govind, stands debited to his personal account.
ii) An amount of ₹ 5,000 withdrawn by the proprietor for his personal use has been debited to trade Expenses A/c
iii) Cash received from Bala ₹ 300 was credited to Balu.
iv) A credit sale of ₹ 2,000 to Janakiram has been wrongly passed through the purchase book.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 37

Question 12.
Rectify the following Errors
i) Repairs made were debited to building account ₹ 5,000
ii) Mahesh networked goods worth ₹ 2,000 no Entry was passed in the Book to this Effects
iii) Purchases of goods from Antony amounting to ₹ 1,500 have been debited to his accounts.
iv) ₹ 5,200 paid for the purchases of the typewriter was charged to the office expenses account.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 38

Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors

Question 13.
Rectify the following Errors
i) Credit purchases of goods from Madhan of ₹ 300 have been wrongly Entered in the sales book.
ii) ₹ 500 received from Seivan has been credited to Selvi’s account
iii) ₹ 1,000 received as interest was credited to the commission account.
iv) Sales book total ₹ 878 was wrongly totaled as ₹ 788.
v) The total of this discount column, on the debit side of the cash book has been added shortly by ₹ 400.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 39

Question 14.
Rectify the following Errors
A Book keeper found his trial balance not balanced, placed the difference amount in the suspense account, and subsequently found the following errors
a) Sales book was overcast by ₹ 1,500
b) ₹ 2900 received from Vani in full settlement of her account of ₹ 3,000 was posted in the cash book but omitted to be entered in her account.
c) The total of the sales book ₹ 12,000 was debited to sales return accounts.
d) ₹ 1,000 received as interest was credited to interest as ₹ 100 Give rectifying entries and show the suspense account.
Solution:
Rectification of Errors
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 40
Suspense Account
Samacheer Kalvi 11th Accountancy Guide Chapter 9 Rectification of Errors 41

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Accountancy Guide Pdf Chapter 8 Bank Reconciliation Statement Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Accountancy Solutions Chapter 8 Bank Reconciliation Statement

11th Accountancy Guide Bank Reconciliation Statement Text Book Back Questions and Answers

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

I. Multiple Choice Questions

Choose the correct answer.

Question 1.
A bank reconciliation statement is prepared by ________.
a) Bank
b) Business
c) Debtor to the business
d) Creditor to the business
Answer:
b) Business

Question 2.
A bank reconciliation statement is prepared with the help of ________.
a) Bank statement
b) Cash book
c) Bank statement and bank column of the cash book
d) Petty cash book
Answer:
c) Bank statement and bank column of the cash book

Question 3.
Debit balance in the bank column of the cash book means ________.
a) Credit balance as per bank statement
b) Debit balance as per bank statement
c) Overdraft as per cash book
d) None of the above
Answer:
a) Credit balance as per bank statement

Question 4.
A bank statement is a copy of ________.
a) Cash column of the cash book
b) Bank column of the cash book
c) A customer’s account in the bank’s book
d) Cheques issued by the business
Answer:
c) A customer’s account in the bank’s book

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 5.
A bank reconciliation statement is prepared to know the causes for the difference between:
a) The balance as per the cash column of the cash book and bank column of the cashbook
b) The balance as per the cash column of the cash book and bank statement
c) The balance as per the bank column of the cash book and the bank statement
d) The balance as per petty cash book and the cash book
Answer:
c) The balance as per the bank column of the cash book and the bank statement

Question 6.
When money is withdrawn from bank, the bank ________.
a) Credits customer’s account
b) Debits customer’s account
c) Debits and credits customer’s account
d) None of these
Answer:
b) Debits customer’s account

Question 7.
Which of the following is not the salient feature of bank reconciliation statement?
a) Any undue delay in the clearance of cheques will be shown up by the reconciliation
b) Reconciliation statement will discourage the accountant of the bank from embezzlement
c) It helps in finding the actual position of the bank balance
d) Reconciliation statement is prepared only at the end of the accounting period
Answer:
d) Reconciliation statement is prepared only at the end of the accounting period

Question 8.
Balance as per cash book is ₹ 2,000. Bank charge of ₹ 50 debited by the bank is not yet shown in the cash book. What is the bank statement balance now?
a) 1,950 credit balance
b) 1,950 debit balance
c) 2,050 debit balance
d) 2,050 credit balance
Answer:
a) 1,950 credit balance

Question 9.
Balance as per bank statement is 1, 000. Cheque deposited, but not yet credited by the bank is 2, 000. What is the balance as per bank column of the cash book?
a) 3,000 overdraft
b) 3,000 favourable
c) 1,000 overdraft
d) 1,000 favourable
Answer:
b) 3,000 favourable

Question 10.
Which one of the following is not a timing difference?
a) Cheque deposited but not yet credited
b) Cheque issued but not yet presented for payment
c) Amount directly paid into the bank
d) Wrong debit in the cash book
Answer:
d) Wrong debit in the cash book

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

II. Very Short Answer Questions

Question 1.
What is meant by bank overdraft?
Answer:
It is not possible to have unfavourable cash balance in the cash book. But, it is possible to have unfavourable balance in the bank account. When the business is not having sufficient money in its bank account, it can borrow money from the bank. As a result of this, the amount is overdrawn from the bank.

Question 2.
What is a bank reconciliation statement?
Answer:
The bank reconciliation statement is a statement that reconciles the balance as per the bank column of the cash book with the balance as per the bank statement by giving the reasons for such difference along with the amount. The internal record of the business (bank column of cash) can be reconciled with the external record (bank statement).

Question 3.
State any two causes of disagreement between the balance as per bank column of cash book and bank statement.
Answer:

  1. Cheques issued but not yet presented for payment.
  2. Cheques deposited into the bank but not yet credited.

Question 4.
Give any two expenses which may be paid by the banker as per standing instruction.
Answer:

  1. Bank Charges
  2. Interest

Question 5.
Substitute the following statements with one word/phrase
(a) A copy of the customer’s account issued by the bank.
(b) Debit balance as per bank statement.
(c) Statement showing the causes of disagreement between the balance as per cash book and balance as per bank statement.
Answer:
(a) Pass book
(b) Pass book favourable
(c) (1) Timing difference, (2) Errors in recording

Question 6.
Do you agree with the following statements? Write “yes” if you agree, and write “no” if you Disagree
Answer:

  1. The bank reconciliation statement is prepared by the banker. – Yes
  2. Adjusting the cash book before preparing the bank reconciliation statement is compulsory. – No
  3. Credit balance as per bank statement is an overdraft. – No
  4. Bank charges debited by the bank increases the balance as per bank statement. – No
  5. Bank reconciliation statement is prepared to identify the causes of differences between balance as per bank column of the cash book and balance as per cash column of the cash book. – Yes

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

III. Short Answer Questions

Question 1.
Give any three reasons for preparing a bank reconciliation statement.
Answer:

  1. To identify the reasons for the difference between the bank balance as per the cash book and bank balance as per bank statement.
  2. To identify the delay in the clearance of cheques.
  3. To ascertain the correct balance of the bank column of the cash book.
  4. To discourage the accountants of the business as well as the bank from misusing funds.

Question 2.
What is meant by the term “cheque not yet presented?”
Answer:

  1. When the cheques are issued by the business, it is immediately entered on the credit side of the cash book by the business.
  2. This may not be entered in the bank statement on the same day.
  3. It will be entered in the bank statement only after it is presented with the bank.

Question 3.
Explain why does money deposited into the bank appears on the debit side of the cash book, but on the credit side of the bank statement?
Answer:
When the cheques are deposited into the bank, the amount is debited in the cash book on the same day. But, these may not be shown in the bank pass book on the same day because these will be entered in the bank statement only after the collection of the cheques.

Question 4.
What will be the effect of interest charged by the bank, if the balance is an overdraft?
Answer:

  1. If the business has taken any loan or overdrawn, interest has to be paid by the business.
  2. The entries for bank charges and interest are made in the bank statement.
  3. The cash book shows more balance than the bank statement.

Question 5.
State the timing differences in BRS with examples.
Answer:
The timing differences in BRS are:

  1. cheques issued but not yet presented for payment
  2. cheques deposited into the bank but not yet credited
  3. bank charges and interest on loan and overdraft
  4. interest and dividends collected by the bank
  5. dishonour of cheques and bills
  6. amount paid by parties directly into the bank
  7. payment made directly by the bank to others
  8. bills collected by the bank on behalf of its customer

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

IV. Exercises

Question 1.
From the following particulars prepare a bank reconciliation statement of Jayakumar as of 31st December 2016.
a) Balance as per cash book ₹ 7,130
b) Cheque deposited but not cleared ₹ 1,000
c) A customer has deposited ₹ 800 into the bank directly
Solution:
Bank reconciliation statement of Jayakumar as of 31st December 2016.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 1

Question 2.
From the following particulars of Kamakshi traders, prepare a bank reconciliation statement as of 31st March 2018.
a) Debit balance as per cash book ₹ 10,500
b) Cheque deposited into bank amounting to ₹ 5,500 credited by bank but entered twice in the cash book
c) Cheques issued and presented for payment amounting to ₹ 7,000 omitted in the cash book
d) Cheque book charges debited by the bank ₹ 200 not recorded in the cash book.
e) Cash of ₹ 1,000 deposited by a customer of the business in cash deposit machine not recorded in the cash book.
Solution:
Bank reconciliation statement of Kamakshi traders as of 31st March 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 2

Question 3.
From the following information, prepare a bank reconciliation statement to find out the bank statement balance as of 31st December 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 3
Solution:
Bank reconciliation statement of Kamakshi traders as on 31st March, 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 4

Question 4.
On 31st March 2017, Anand’s cash book showed a balance of ₹ 1,12,500, Prepare bank reconciliation statement,
a) He had issued cheques amounting to ₹ 23,000 on 28,3.2017, of which cheques amounting to ₹ 9,000 have so far been presented for payment.

b) A cheque for ₹ 6,300 deposited into bank on 27.3.2017, but the bank credited the same only on 5th April 2017.

c) He had also received a cheque for ₹ 12,000 which, although entered by him in the cash book, was not deposited in the bank.

d) Wrong credit given by the bank on 30th March 2017 for ₹ 2,000.

e) On 30th March 2017, a bill already discounted with the bank for ₹ 3,000 was dishonoured, but no entry was made in the cash book.

f) Interest on debentures of ₹ 700 was received by the bank directly.

g) Cash sales of ₹ 4,000 wrongly entered in the bank column of the cash book.
Solution:
Bank reconciliation statement of Mr, Anand as on 31st March, 2017
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 5

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 5.
From the following particulars of Siva and Company, prepare a bank reconciliation statement as of 31st December 2017.
a) Credit balance as per cash book ₹ 12,000
b) A cheque of ₹ 1,200 Issued and presented for payment to the bank, wrongly credited in the cash book
c) Debit side of bank statement was undercast by ₹ 100
Solution:
Bank reconciliation statement as of 31st December 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 6

Question 6.
From the following particulars of Raheem traders, prepare a bank reconciliation statement as of 31st March 2018.
a) Overdraft as per cash book ₹ 2,500
b) Debit side of cash book was under cash by ₹ 700
c) Amount received by the bank through RTGS amounting to ₹ 2,00,000, omitted in the cash book.
d) Two cheques issued for ₹ 1,800 and ₹ 2,000 on 29th March 2018. Only the second cheque is presented for payment.
e) Insurance premium on the car for ₹ 1,000 paid by the bank as per standing instruction not recorded in the cash book
Solution:
Bank reconciliation statement as of 31st March 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 7

Question 7.
From the following information, prepare a bank reconciliation statement as of 31st December,
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 8
Solution:
Bank reconciliation statement as on 31st December, 2017
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 9

Question 8.
Prepare bank reconciliation statement from the following data.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 10
Solution:
Bank reconciliation statement
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 11

Question 9.
From the following particulars of Veera traders, prepare a bank reconciliation statement as on 31st December, 2017.
a) Credit balance as per bank statement ₹ 6,000
b) Amount received by bank through NEFT for ₹ 3,500, entered twice in the cash book.
c) Cheque dishonoured amounting to ₹ 2,500, not entered in cash book.
Solution:
Bank reconciliation statement as on 31st December, 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 12

Question 10.
Prepare bank reconciliation statement from the following data and find out the balance as per cash book as on 31st March, 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 13
Solution:
Bank reconciliation statement as on 31st March, 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 14

Question 11.
Ascertain the cash book balance from the following particulars as of 31st December 2017
i) Credit balance as per bank statement ₹ 2,500
ii) Bank charges of ₹ 60 have not been entered in the cash book
iii) Cheque deposited on 28th December 2017 for ₹ 1,000 was not yet credited by the bank
iv) Cheque issued on 24th December 2017 for ₹ 700, not yet presented for payment
v) A dividend of ₹ 400 collected by the bank directly but not entered in the cash book
vi) A cheque of ₹ 600 had been dishonoured, but no entry was made in the cash book
vii) Interest on term loan ₹ 1,200 debited by the bank but not accounted in the cash book
viii) No entry had been made in the cash book for a trade subscription of ₹ 500 paid vide banker’s order on 23rd December 2014
Solution:
Bank reconciliation statement as of 31st December 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 15

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 12.
From the following particulars of Raja traders, prepare a bank reconciliation statement as on 31st January, 2018.
a) Balance as per bank statement ₹ 5,000

b) Cheques amounting to ₹ 800 had been recorded in the cash book as having been deposited into the bank on 25th January 2018, but were entered in the bank statement on 2nd February 2018.

c) Amount received by bank through NEFT amounting to ₹ 3,000, omitted in the cash book.

d) Two cheques issued for ₹ 3,000 and ₹ 2,000 on 29th March 2018. Only the first cheque is presented for payment.

e) Insurance premium on motor vehicles for ₹ 1,000 paid by the bank as per standing instruction not recorded in the cash book.

f) Credit side of cash book was undercast by ₹ 700

g) Subsidy received directly by the bank from the state government amounting to ₹ 10,000, not entered in the cash book.
Solution:
Bank reconciliation statement of Mr. Raja traders as of 31st January 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 16

Question 13.
From the following particulars of Simon traders, prepare a bank reconciliation statement as on 31st March 2018.
a) Debit balance as per bank statement ₹ 2,500
b) Cheques deposited amounting to ₹ 10,000, not yet credited by the bank.
c) Payment through net banking for ₹ 2,000, omitted in the cash book.
Solution:
Bank reconciliation statement as on 31st March 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 17

Question 14.
From the following particulars, ascertain the cash book balance as on 31st December 2016.
i) Overdraft balance as per bank statement ₹ 1,26,640
ii) Interest on overdraft entered in the bank statement, but not yet recorded in cash book ₹ 3,200
iii) Bank charges entered in the bank statement, but not found in cash book ₹ 600
iv) Cheques issued, but not yet presented for payment ₹ 23,360
v) Cheques deposited into the bank but not yet credited ₹ 43,400
vi) Interest on investment collected by the bank ₹ 24,000
Solution:
Bank reconciliation statement as of 31st December 2016.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 18

Question 15.
From the following particulars of John traders, prepare a bank reconciliation statement as on 31st March, 2018.
a) Bank overdraft as per bank statement ₹ 4,000

b) Cheques amounting to ₹ 2,000 had been recorded in the cash book as having been deposited into the bank on 26th March 2018 but were entered in the bank statement on 4th April 2018.

c) Amount received by the bank through cash deposit machine amounting to ₹ 5,000, omitted in the cash book.

d) Amount of ₹ 3,000 wrongly debited to John traders account by the bank, for which no details are available.

e) Bills for collection credited by the bank till 29th March 2017 amounting to ₹ 4,000, but no advice received by John traders.

f) Electricity charges made through net banking for ₹ 900 were wrongly entered in the cash column of the cash book instead of the bank column.
Solution:
Bank reconciliation statement as of 31st March 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 19

Question 16.
Prepare bank reconciliation statement from the following data.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 20
Solution:
Prepare bank reconciliation statement.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 21

Question 17.
Prepare bank reconciliation statement as of 31st March 2017 from the following extracts of cash book and bank statement.
Cashbook (Bank column only)
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 22
Bank statement
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 23
Solution:
Bank reconciliation statement as on 31st March, 2017
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 24

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 18.
A trader received his bank statement on 31st December 2017 which showed an overdraft balance of ₹ 12,000. On the same day, his cash book showed a debit balance of ₹ 2,000.
Analyze the following transactions. Choose the possible causes and prepare a bank reconciliation statement to show the causes of differences.
a) Cheque deposited for ₹ 2,000 on 21st December 2017. The bank credited the same on 26th December 2017.

b) Cheque issued for payment on 26th December 2017 amounting to ₹ 2,500, not yet presented until 31st, December 2017.

c) Bank charges amounting to ₹ 200 not yet entered in the cash book.

d) Online payment for ₹ 1,500 entered twice in the cash book.

e) Cheque deposited amounting to ₹ 1,000, but omitted in the cash book. The same cheque was dishonoured by bank, but not yet entered in the cash book.

f) Cheque deposited, not yet credited by bank amounting to ₹ 17,800.
Solution:
Bank reconciliation statement as of 31st December 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 25

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

11th Accountancy Guide Bank Reconciliation Statement Additional Important Questions and Answers

I. Choose the correct answer.

Question 1.
A Bank Reconciliation Statement is prepared with the help of ________.
a) Bank statement and bank column of the cash book
b) Journal
c) Ledger
d) None of the above
Answer:
a) Bank statement and bank column of the cash book

Question 2.
Bank reconciliation statement is ______
a) Part of bank statement
b) Part of the cash book
c) A separate statement
d) A sub-division of journal
Answer:
a) Part of bank statement

Question 3.
Uncollected cheques are also known as ______.
a) Outstanding cheques
b) Uncleared cheques
c) Outstation cheques
d) Both a & c
Answer:
d) Both a & c

Question 4.
When a cheque is not paid by the bank it is called as ______.
a) Honoured
b) Endorsed
c) Dishonoured
d) None of these
Answer:
c) Dishonoured

Question 5.
A bank reconciliation statement is prepared by ______.
a) Banker
b) Accountant of the business
c) Auditors₹
d) None of the above
Answer:
b) Accountant of the business

Question 6.
The cheque which is deposited into the bank but not cleared at the end of a particular year is called ______.
a) Uncredited cheque
b) Unpresented cheque
c) Omitted cheque
d) Dishonoured cheque
Answer:
b) Unpresented cheque

Question 7.
In cash book bank charges recorded in the ______.
a) Credit side
b) Debit Side
c) Both a & b
d) None of the above
Answer:
a) Credit side

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 8.
An amount of Rs,2G0Q is debited twice in the bank statement. What will the reflect when overdraft as per the cash book is the starting point ______.
a) ₹ 2000 will be deducted
b) ₹ 2000 will be added
c) ₹ 4000 will be deducted
d) ₹ 4000 will be deducted
Answer:
b) ₹ 2000 will be added

Question 9.
If any amount is directly deposited into the bank then ______.
a) Cashbook will show less balance & bank book will show more
b) Cashbook will show more balance & bank book will show less
c) Cashbook will show double balance
d) Bank book will show double
Answer:
a) Cashbook will show less balance & bank book will show more

Question 10.
Which of the following error results in an unadjusted cash book balance?
a) Outstanding cheques
b) Unpresented Cheques
c) deposit in Transit
d) Omission of Bank charges
Answer:
d) Omission of Bank charges

Question 11.
Credit balance in the bank column of the cash book means ______.
a) Credit balance as per bank statement
b) Debit balance as per bank statement
c) Overdraft as per cash book
d) None of the above
Answer:
b) Debit balance as per bank statement

Question 12.
When balance as per Cash Book is the starting point, to ascertain balance as per bank statement interest allowed by Bank is ______.
a) Subtracted
b) added
c) not adjusted
d) None of the above
Answer:
b) added

Question 13.
When balance as per Cash Book is the starting point, to ascertain the balance as per bank statement interest charged by Bank is:
a) Added
b) subtracted
c) not adjusted
d) None of the above
Answer:
b) subtracted

Question 14.
When the balance as per Cash Book is the starting point to ascertain balance as per bank statement, direct deposits by customers are:
a) Added
b) subtracted
c) not adjusted
d) None of the above
Answer:
a) Added

Question 15.
When the balance as per Cash Book is the starting point to ascertain balance as per bank statement, direct payments by the bank are:
a) Added
b) subtracted
c) not adjusted
d) None of the above
Answer:
b) subtracted

Question 16.
______ is not possible to have unfavourable cash balance in the cash book.
a) Bank statement
b) Bank overdraft
c) Cash overdraft
d) Cashbook
Answer:
b) Bank overdraft

Question 17.
Bank overdraft is available only to the ______ holders.
a) Saving Account
b) Fixed Account
c) Joint Account
d) Current Account
Answer:
d) Current Account

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 18.
______ is simply a copy of the customer’s account in the books of a bank.
a) Cashbook
b) Bank statement
c) Bank Account
d) None of these
Answer:
b) Bank statement

Question 19.
A bank statement is a copy of ______.
a) the cash column of a customer’s cash book
b) the bank column of a customer’s cash book
c) the customer’s account in the bank’s ledger
d) None of these
Answer:
c) the customer’s account in the bank’s ledger

Question 20.
Debit balance in the Cash Book means ______.
a) overdraft as per bank statement
b) credit balance as per bank statement
c) overdraft as per Cash Book
d) None of these
Answer:
b) credit balance as per bank statement

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

II. Additional Questions & Answers

Question 1.
Differences between bank column of cash book and bank statement.
Answer:
Bank column of cash book:

  • It is prepared by a business concern.
  • Cash deposits are entered on the debit side.
  • Cash withdrawals are entered on the credit side.
  • Cheque deposits are debited on the day of the deposit.
  • Cheques issued are credited on the day of the issue of the cheque.
  • Collections and payments as per standing instructions of the business are entered only after checking with the bank statement.
  • It is balanced at the end of a specific period.

Bank statement:

  • It is prepared by a bank (banker).
  • Cash deposits are entered in the credit column.
  • Cash withdrawals are entered in the debit column.
  • Cheque deposits are credited only at the time of realization of the cheque.
  • Cheques issued by customers are debited by the bank on the date on which the payment is made.
  • Collections and payments as per standing instructions of the business are entered in the banker’s book on the date of realization of payment.
  • It is balanced after each transaction.

Question 2.
What are the items recorded on the debit side of the bank column of the cash book?
Answer:

  1. Cheques deposited but not credited.
  2. Credits in the passbook only.
    • Interest credited in the bank statement
    • Dividend and other income
    • • Direct deposit by a party
  3. Any error in the cash book/ bank statement has the effect of increasing the balance as per the bank statement.

Question 3.
What are the items recorded on the credit side of the bank column of the Cash Book?
Answer:

  1. Cheques deposited but not credited
  2. Cheques dishonoured but not entered in the cash book
  3. Debits in bank statement only
    • Interest debited
    • Insurance premium, loan instalment, etc., paid as per standing instructions
    • Direct payment by banker
  4. Any error in cash book/ bank statement which has the effect of decreasing the balance as per bank statement

Question 4.
What is meant by the term “Cheques deposited into bank but not yet credited?”
Answer:
When the cheques are deposited into bank, the amount is debited in the cash book on the same day. But, these may not be shown in the bank pass book on the same day because these will be entered in the bank statement only after the collection of the cheques.

For example, the balances as per cash book and bank statement are ₹ 20,000 for X & Co. X & Co. receives a cheque on 25th March 2016, from ABC Limited for ₹ 5,000. On the same day, X & Co, debits its cash book with ₹ 5,000.

But bank credits X & Co’s account only when the cheque is collected from ABC Limited’s bank. This shows that is a time gap between depositing the cheque by the customer (X & Co) and collection of cheque by the bank.

Question 5.
What will be the effect of Interest and dividends collected by the bank?
Answer:
The bank may collect dividends on its customer’s investment in shares and also interest on any investment. The entry for this will be made in the bank statement on the date of collection. But the entry is made in the cash book only when the bank statement is received by the customer. Till then, the cash book shows less balance than the bank statement.

Question 6.
What will be the effect of Dishonour of cheques and bills?
Answer:
When the cheque is received from outside parties, it is deposited with the bank and debited in the cash book. If the cheque is dishonoured, the bank cannot collect the amount of such cheque from outside parties’ bank. It is not credited in the bank statement. As a result of this, the two records would differ.

While discounting the bills receivables, in the cash book it is entered in the debit side and in the bank statement it is credited. When the bill is presented by the bank to the drawee of the bill and the payment is not received, the bank debits the same to cancel the credit.

But, credit is made in the cash book only when the customer gets the entries made in the bank statement is received. The bank may also charge some amount for such dishonour.

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 7.
What will be the effect of Amount paid by parties directly into the bank?
Answer:
Sometimes, debtors or the customers of the business may directly deposit the money into bank account of the business. It may be done by directly visiting the branch of the bank by paying cash (including NEFT, RTGS) or swiping debit or credit or business card or depositing the money in cash deposit machine or transfer through online banking facility.

This will be credited in the banker’s book. But the entry is made in the cash book only when the bank statement is received by the customer. Until then, the cash book shows less balance than bank statement.

Question 8.
What will be the effect of Amount paid directly by the bank to others?
Answer:
Sometimes the bank may be instructed to make payments such as, insurance premium, instalment of loan, etc., as an agent of the customer on behalf of its customer. In all such cases, debit is made in bank statement. But, the entry is made in the cash book only when the bank statement is received by the customer. Till then, the cash book shows more balance than bank statement.

Question 9.
What will be the effect of Bills collected by the bank on behalf of its customers?
Answer:
When goods are sold by the business, the documents may be sent through the bank. When the bank collects the amount, it is credited in bank records. But, the entry is made in the cash book only when the bank statement is received by the business. Till then, the bank statement shows more balance than cash book.

Question 10.
Explain the differences arising due to errors in recording the entries.
Answer:
Errors committed in recording the transactions by the business in the cash book:
Sometimes, errors may be committed in the cash book. For example, omission or wrong recording of transaction relating to cheques deposited or issued, wrong balancing, etc. In these cases, obviously, there will be differences between bank balance as per bank statement and bank balance as per cash book.

Errors committed in recording the transactions by the bank:
Sometimes errors may be committed in the banker’s book. For example, omission or wrong recording of transaction relating to cheques deposited and wrong balancing. In these cases, obviously, there will be differences between bank balance as per bank statement and bank balance as per cash book.

Question 11.
What is the need for bank reconciliation statement?
Answer:

  1. To identify the reasons for the difference between the bank balance as per the cash book and bank balance as per bank statement.
  2. To identify the delay in the clearance of cheques.
  3. To ascertain the correct balance of bank column of cash book.
  4. To discourage the accountants of the business as well as bank from misusing funds.

Additional Sums:

Question 1.
Prepare bank reconciliation statement of Mr. Bala as on 31.03.2013.
a) Balance as per cash book ₹ 15,000
b) Cheques deposited but not cleared ₹ 1,000
c) Cheques issued but not yet present for payments ₹ 1500 d. Interest allowed by bank ₹ 200
Solution:
Prepare bank reconciliation statement
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 26

Question 2.
Prepare bank Reconciliation statement to find out balance as per bank statement on 31st March 2018,
1. Cheques deposited but not yet collected by the bank ₹ 1,000
2. Cheques issued but not yet presented for payment ₹ 2,000
3. Bank Interest Charged ₹ 200
4. Rent paid by bank as per standing Instruction ₹ 400
5. Cash book balances ₹ 600
Solution:
Prepare bank reconciliation statement
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 27

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 3.
Form the following particulars of Ashok and company; prepare a bank reconciliation statement as on 31st March 2018.
a) Credit balance as per cash book ₹ 10,000
b) Cheques issued but not yet presented for payment ₹ 10,000
c) Cheques Deposited but not credited ₹ 9000
d) Rent collected by the bank as per standing Instruction ₹ 500
Solution:
Bank Reconciliation statement Mr. Ashok as on 31st March 2018
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 28

Question 4.
From the following information, Prepare bank Reconciliationstatement of Mr. Mohan as on 31st Dec. 2017 to find out the balance as per bank statement.
i) Overdraft as per cash book – 20000
ii) Cheques deposited but not yet credited – 10000
iii) Amount wrongly deposited by bank – 600
iv) Interest on overdraft debited by bank – 2000
v) Cheque issued but not yet present for payment – 2000
vi) Payment received from the customer directly by the bank – 1000
Solution:
Bank Reconciliation statement Mr. Mohan as on 31st Dec. 2018.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 29

Question 5.
Prepare bank Reconciliation statement as on 31st December 2017. From the following in information.
a) Balance as perbank statement (pass book) is ₹ 50,000
b) Cheques deposited into bank amount into ₹ 7,000 were not yet collected.
c) Bank charges of ₹ 600 have not been entered in the cash book.
d) Cheques issued amount to ₹ 18,000 have not been presented by for payment.
Solution:
Bank Reconciliation statement as on 31st Dec. 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 30

Question 6.
From the following information, prepare bank Reconciliationstatement as of Mr. Pugazh as on 31st Dec. 2017.
i) Credit balance as per bank statement ₹ 12,000
ii) Cheques deposited on 28th December 2017 but not yet credited ₹ 4000
iii) Cheques issued for 20000 on 20th December 2017 but not yet presented for payment 6000.
iv) Interest on debentures directly in cash book ₹ 8000
v) Insurance premium on building directly paid by the bank ₹ 2000
vi) Amount wrongly credit by bank ₹ 1,000
Solution:
Bank Reconciliation statement of Mr. Pugazh as on 31st Dec. 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 31

Question 7.
From the following data, as certain the cash book balance as on 31st Dec. 2017.
1) Overdraft balance as per bank statement ₹ 13,000
2) Cheques deposited into the bank but not yet credited ₹ 21,000
3) Wrongly credit by the bank ₹ 1,000
4) Cheques issued, but not yet presented for payment₹ 6,000
5) Bank charges debited by bank ₹ 360
6) Insurance Premium on building directly paid by bank ₹ 200
Solution:
Bank Reconciliation statement on 31st Dec. 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 32

Question 8.
Prepare bank Reconciliation statement as on 31st Dec. 2017, From the following balance of cash book, and bank statement.
Cash book (Bank column)
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 33
Bank Statement
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 34
Solution:
Bank Reconciliation Statement on 31st Dec, 2017.
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 35

Question 9.
On 31st March 2017, the pass book of Mr, A showed a credit balance of Rs.92,500. A comparison of pass book and cash book revealed the following:
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 36
Solution:
Bank Reconciliation Statement of Mr. A as on 31st March 2017
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 37

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 10.
The bank overdraft of Rajini on 31.12.2017 as per cash book is 90,000. From the following particulars, prepare bank reconciliation statement:
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 38
Solution:
Bank Reconciliation Statement as on 31,12.2017 3,000
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 39

Question 11.
Prepare a bank reconciliation statement from the following data as on 31.12.2017.
a) Balance as per cash book ₹ 1,25,500
b) Cheques issued but not presented for payment ₹ 9,000
c) Cheques deposited in bank but not collected ₹ 12,000
d) Bank paid insurance premium ₹ 5,000
e) Direct deposit by a customer ₹ 8,000
f) Interest on investment collected by bank ₹ 2,000
g) Bank charges ₹ 1,000
Solution:
Bank Reconciliation Statement as on 31.12.2017
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 41

Question 12.
The pass book of X with his bank shows a debit balance of Rs. 500 on 31.10.2017. On comparison of the pass book with the cash book, it is observed that:
i. Cheques issued by X in October 2017 amounted to ₹ 4, 535 of which cheques amounting to ₹ 3,535 were paid by the bank by 31st October 2017.

ii. X deposited cheques amounting to ₹ 5, 000 on 31st October 2017. These cheques were realised by the bank on 1st November, 2017.

iii. Y a customer of X had directly deposited a sum of ₹ 3, 000 on 24th October 2017 to the credit of X account with the bank. X recorded this receipt on 4th November, 2017.

iv. The bank had debited X’s account with ₹ 1, 520 on 31.1.2017 on account of a dishonoured bill. No entry for the same has been made in the account books.

v. On 31.10.1995 X’s account was credited with ₹ 130 being dividend collected by the bank. On the same day, his account was debited with ₹ 10 being bank charges. Both these entries were recorded by X only on 5th November, 2017.
Prepare the Bank Reconciliation Statement as at 31.10.2017.
Solution:
Bank Reconciliation Statement as on 31.10.2017
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 42

Question 13.
From the following particulars ascertain the bank balance as would appear in the pass‘book as on 31st December, 2016.
i. The bank overdraft (Credit balance) as per cash book on 31st December 2016 was ₹ 60,000
ii. Interest on overdraft, six months ending 31st December, amounting to ₹ 2,000 is debited in the pass book.
i. Bank charges for the above period also debited in the pass book which amounted to ₹ 500.
ii. Cheques issued but not presented for payment before 31st December amounted to ₹ 15,000.
iii. Cheques paid into the bank, but not cleared and credited before 31st December were ₹ 25,000.
iv. Interest on government securities collected by the bank and credited in the pass book amounted to ₹ 18,000.
Solution:
Bank Reconciliation Statement as on 31st March 2016
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 43

Question 14.
From the following information available from the books and records of X & Co., prepare BRS:
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 44
Solution:
Bank Reconciliation Statement for Bank A/c No. I
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 45
Bank Reconciliation Statement for Bank A/c No. II
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 46

Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement

Question 15.
From the following particulars ascertain the bank balance that would appear in the cash book of Son 31.12.2016.
i) The bank overdraft as per pass book on 31.12.2016 ₹ 6,340
ii) Interest on on for the year ending 31.12.2016 ₹ 160 is debited in the pass book
iii) Bank charges of ₹130 for the above period are also debited in the pass book.
iv) Cheques issued but not cashed prior to 31.12.2016 amounted to ₹ 11,168
v) Cheques paid into bank but not cleared before 31.12.2016 were ₹ 2170
vi) Interest on investments collected by the bankers and credited in the pass book, ₹ 1,200
Solution:
Bank Reconciliation Statement as on 31st December 2016
Samacheer Kalvi 11th Accountancy Guide Chapter 8 Bank Reconciliation Statement 47

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 10 Operations Research Miscellaneous Problems Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Miscellaneous Problems

Question 1.
The following table summarizes the supply, demand and cost information for four factors S1, S2, S3, S4 Shipping goods to three warehouses D1, D2, D3.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 1
Find an initial solution by using north west corner rule. What is the total cost for this solution?
Solution:
The given transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 2
Here total supply = 5 + 8 + 7+14 = 34
Total amount =7 + 9 + 18 = 34
(i.e) Total supply = Total demand.
∴ The given problem is balanced transformation problem.
We can find an initial basic feasible solution to the given problem.
First allocation:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 3
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 4
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 5
Transportation schedule:
S1 → D1; S2 → D1; S2 → D2;
S3 → D2; S3 → D3; S4 → D3
The transportation cost:
= (5 × 2) + (2 × 3) + (6 × 3) + (3 × 4) + (4 × 7) + (14 × 2)
= 10 + 6 + 18 + 12 + 28 + 28
= 102

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Question 2.
Consider the following transportation problem
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 6
Determine an initial basic feasible solution using (a) Least cost method (b) Vogel’s approximation method.
Solution:
(a) Least cost method
Given transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 7
Total Availability = Total Requirement = 100
∴ The given problem is balanced transformation problem.
Hence there exists a feasible solution to the given problem
First allocation:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 8
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 9
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 10
Here
x12 = 10; x13 = 20; x21 = 30;
x22 = 10; x24 = 10; x32 = 20
Transportation Scheme:
O1 → D2; O1 → D3; O2 → D1;
O2 → D2; O2 → D4; O3 → D2
The transportation cost:
=(10 × 8) + (20 × 3) + (30 × 4) + (10 × 5) + (10 × 4) + (20 × 2)
= 80 + 60 + 120 + 50 + 40 + 40
= 390

(ii) Vogel’s approximation method:
Here Σai = Σbj = 100
∴ The given problem is balanced transformation problem.
Hence there exists a feasible solution to the given problem
First allocation:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 11
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 12
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 13
Here
x11 = 30; x13 = 20; x22 = 20;
x24 = 10; x32 = 20
Transportation Scheme:
O1 → D1; O2 → D3; O2 → D2;
O2 → D4; O3 → D2;
Total transportation cost:
= (30 × 5) + (20 × 3) + (20 × 5) + (10 × 4) + (20 × 2)
= 150 + 60 + 100 + 40 + 40
= 390

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Question 3.
Determine an initital basic feasible solution to the following transportation problem by using (i) North West Corner rule (ii) least cost method.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 14
Solution:
(i) North West Corner rule:
The given transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 15
Total supply = 25 + 35 + 40 = 100
Total Requirement = 30 + 25 + 45 + 100
(i.e) Total supply = Total requirement.
∴ The given problem is balanced transformation problem.
Hence there exists a feasible solution to the given problem
First allocation:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 16
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 17
Transformation schedule:
S1 → D1; S2 → D1; S2 → D2;
S3 → D3; S3 → D3;
The transformation cost:
= (25 × 9) + (5 × 6) + (25 × 8) + (5 × 4) + (40 × 9)
= 225 + 30 + 200 + 20 + 360 = 835

(ii) Least cost method
The given transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 18
(i.e) Total supply = Total requirement = 100
∴ The given problem is balanced transformation problem.
Hence there exists a feasible solution to the given problem
First allocation:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 19
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 20
Transportation schedule:
S1 → D3; S2 → D3; S3 → D1
S3 → D2;
The transportation cost:
= (10 × 5) + (35 × 4) + (15 × 7) + (25 × 6) + (40 × 9)
= 50 + 140 + 105 + 150 + 360 = 805

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Question 4.
Explain Vogel’s approximation method by obtaining initial basic feasible solution of the following transportation problem.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 21
Solution:
The given transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 22
Here Σai = Σbj =17
(i.e) Total supply = Total Demand
∴ The given problem is balanced transformation problem.
Hence there exists a feasible solution to the given problem
First allocation:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 23
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 24
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 25
Here
x11 = 1; x12 = 5; x24 = 1;
x31 = 6; x33 = 15;
Transportation schedule:
O1 → D1; O1 → D2; O2 → D4
O3 → D1; O3 → D3
The transportation cost:
=(1 × 2) + (5 × 3) + (1 × 1) + (6 × 5) + (3 × 15) + (1 × 9)
= 2 + 15 + 1 + 30 + 45 + 9
= 102

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Question 5.
A car hire company has one car at each of five depots a,b,c,d and e. A customer in each of the fine towers A, B, C, D and E requires a car. The distance (in miles) between the depots (origins) and the towers (destinations) where the customers are given the following distance matrix.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 26
How should the cars be assigned to the customers so as to minimize the distance travelled?
Solution:
Here the number of rows and columns are equal.
∴ The given assignment problem is balanced.
Step 1.
Select the smallest element in each row and subtract this from all the elements in its row.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 27

Step 2.
Select the smallest element in each column and subtract this from all the elements in its column.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 28

Step 3. (Assignment)
Examine the rows with exactly one zero, mark the zero by □ mark other zeros, in its column by X
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 29

Step 4.
Now Examine the rows with exactly one zero, mark the zero by □ mark other zeros, in its column by X
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 30

Step 5.
Cover all the zeros of table 4 with three lives. Since three assignments were made please note that check [✓] Row C and E which have no assignment.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 31

Step 6.
Develop the new revised tableau. Examine those elements that are not covered by a line in Table 5. Take the smallest element in each row and subtract from the uncovered cells, depots
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 32

Step 7.
Go to step 3 and repeat the procedure until you arrive at an optimal assignments.
depots

Step 8.
Determine an assignment
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 33
Here all the five assignments have been made. The optimal assignment schedule and total distance is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 34
∴ The optimum Distance (minimum) 575 kms

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Question 6.
A natural truck – rental service has a surplus of one truck in each of the cities 1, 2, 3, 4, 5 and 6 and a deficit of one truck in each of the cities 7, 8, 9, 10, 11 and 12. The distance (in kilometers) between the cities with a surplus and the cities with
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 35
How should the truck be dispersed so as to minimize the total distance travelled?
Solution:
Here the number of rows and columns are equal.
∴ The given assignment problem is balanced.
Step 1.
Select the smallest element in each row and subtract this from all the elements in its row.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 36

Step 2.
Select the smallest element in each column and subtract this from all the elements in its column.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 37

Step 3.
Examine the rows with exactly one zero, mark the zero by □ mark other zeros, in its column by X
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 38

Step 4.
Examine the Columns with exactly one zero. If there is exactly one zero, mark that zero by □ mark other zeros in its rows by X
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 39

Step 5.
Cover all the zeros of table 4 with five lines. Since three assignments were made
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 40

Step 6.
Develop the new revised tableau. Examine those elements that are not covered by a line in Table 5. Take the smallest element. This is l(one) in our case. By subtracting 1 from the uncovered cells.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 41

Step 7.
Go to step 3 and repeat the procedure until you arrive at an optimal assignments.

Step 8.
Determine an assignment
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 42
Here all the six assignments have been made. The optimal assignment schedule and total distance is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 43
∴The optimum Distance (minimum) = 125 kms

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Question 7.
A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay – off matrix based on three potential economic conditions is given in the following table
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 44
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems 45
(i) Maximin
Max (3000, 1000, 6000) = 6000. Since the maximum pay of is 6000, the alternative ‘Debentures’, is selected.

(ii) Minimax
Min (10000, 8000, 6000) = 6000, Since the minimum pay-off is 6000. the alternative ‘Debentures’ is selected.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Miscellaneous Problems

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 10 Operations Research Ex 10.4 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.4

Choose the correct answer

Question 1.
The transportation problem is said to be unbalanced if
(a) Total supply ≠ Total demand
(b) Total supply = Total demand
(c) m = n
(d) m + n – 1
Solution:
(a) Total supply ≠ Total demand

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Question 2.
In a non – degenerate solution number of allocation is
(a) Equal to m + n – 1
(b) Equal to m + n + 1
(c) Not equal to m + n – 1
(d) Not equal to m + n + 1
Solution:
(a) Equal to m + n – 1

Question 3.
In a degenerate solution number of allocations is
(a) Equal to m + n – 1
(b) Not equal to m + n – 1
(c) Less then m + n – 1
(d) Greater then m + n – 1
Solution:
(c) Less then m + n – 1

Question 4.
The Penalty in VAM represents difference between the first
(a) Two largest costs
(b) Largest and Smallest costs
(c) smallest two costs
(d) None of these
Solution:
(c) smallest two costs

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Question 5.
Number of basic allocation in any row or column in an assignment problem can be
(a) Exactly one
(b) At least one
(c) At most one
(d) None of these
Solution:
(a) Exactly one

Question 6.
North – West Corner refers to
(a) Top left corner
(b) Top right corner
(c) Bottom right corner
(d) Bottom left corner
Solution:
(a) Top left corner

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Question 7.
Solution for transportation problem using method is nearer to an optimal
(a) NWCM
(b) LCM
(c) VAM
(d) Row Minima
Solution:
(c) VAM

Question 8.
In an assignment problem the value of iedsion variable xij is
(a) 1
(b) 0
(c) 1 or 0
(d) none of them
Solution:
(c) 1 or 0

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Question 9.
If number of sources is not equal to number of destinations, the assignment problem is called
(a) balanced
(b) unsymmetric
(c) symmetric
(d) unbalanced
Solution:
(d) unbalanced

Question 10.
The purpose of a dummy row or column in an assignment problem is to
(a) prevent a solution from becoming degenerate
(b) balance between total activities and total resources
(c) provide a means of representing a dummy problem
(d) None of the above
Solution:
(b) balance between total activities and total resources

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Question 11.
The solution for an assignment problem is optimal if
(a) each row and each column has no assignment
(b) each row and each column has atleast one assignment
(c) each row and each column has atmost one assignment
(d) each row and each column has exactly one assignment
Solution:
(d) each row and each column has exactly one assignment

Question 12.
In an assignment problem involving four workers and three jobs, total number of assignments possible are
(a) 4
(b) 3
(c) 7
(d) 12
Solution:
(b) 3

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Question 13.
Decision theory is concerned with
(a) analysis of information that is available
(b) decision making under certainty
(c) selecting optimal decisions in sequential problem
(d) All of the above
Solution:
(d) All of the above

Question 14.
A type of decision – making environment is
(a) certainty
(b) uncertainty
(c) risk
(d) all of the above
Solution:
(d) all of the above

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.4

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 10 Operations Research Ex 10.3 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3

Question 1.
Given the following pay – off matrix (in rupees) for three strategies and two states for nature.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 1
Select a strategy using each of the following rule (i) Maximin (ii) Minimax
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 2
(i) Max min
Max ( 40, -20, -40) = 40. Since the maximum pay-off is 40, the alternative S, is selected.

(ii) Minimax
min (60, 10, 150) = 10, Since the minimum payoff is 10. the alternative S2 is selected.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3

Question 2.
A farmer wants to decide which of three crops he should plant on his 100 – acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 3
In the farmer wishes to plant only crop, decide which should be his best crop using (i) Maximin (ii) Minimax
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 4
(i) Maximin
Max ( 3500, 4500, 2000) = 4500. Since the maximum pay-off is 4500, the alternative ‘Medium’, is selected.

(ii) Minimax
min (8000, 5000, 5000) = 5000, Since the minimum pay-off is 5000. the alternatives both ‘Medium’ and ‘Low’ are selected.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3

Question 3.
The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following T estimated pay-offs for various level of sales.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 5
What will be the marketing manager’s decision if (i) Maximin and (ii) Minimax principle applied?
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 6
(i) Maximin
Max ( 10, 5, 3) = 10. Since the maximum pay of is 10, “Egg Shampoo”, is selected.

(ii) Minimax
min (30, 40, 55) = 30, Since the minimum pay-off is 30. the alternative “Egg Shampoo” is selected

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3

Question 4.
Following pay – off matrix, which is the optimal decision under of the following rule (i) maximin (ii) minimax
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 7
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3 8
(i) Maximin
Max ( 5, 7, 9, 8) = 5. Since the maximum pay-off is 5, the alternative A1 is selected.

(ii) Minimax
min (14, 11, 11, 13) = 11, Since the minimum pay-off is 11. the alternative alternatives A2 and A3 are selected.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.3

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 10 Operations Research Ex 10.2 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.2

Question 1.
What is the Assignment problem?
Solution:
Suppose that we have ‘m1 jobs to be performed on ‘n’ machines. The cost of assigning each job to each machine is Cij (i = 1, 2, … n and j = 1, 2, … , n). Our objective is to assign the different jobs to the different machines (one job per machine) to minimize the overall cost. This is known as an assignment problem.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Question 2.
Give mathematical form of assignment problem.
Solution:
Consider the problem of assigning n jobs to n machines (one job to one machine). Let Cij be the cost of assigning ith job to the jth machine and xij represents the assignment of ith job to the jth machine.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 1
xij is missing in any cell means that no assignment is made between the pair of job and machine.(i.e) xij = 0.
xij is present in any cell means that an assignment is made their. In such cases xij = 1
The assignment model can written in LPP as follows
Minimize Z = \(\sum_{i=1}^{m}\) \(\sum_{j=1}^{n}\) Cij xij
Subject to the constrains
\(\sum_{i=1}^{n}\) xij = 1, j = 1, 2, …. n
\(\sum_{j=1}^{n}\) xij = 1, i = 1,2,….n and xij =0 (or) 1 for all i, j

Question 3.
What is the difference between Assignment Problem and Transportation Problem?
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 2

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Question 4.
Three jobs A, B, and C one to be assigned to three machines U, V, and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.
(cost is in Rs per unit)
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 3
Solution:
Here the number of rows and columns are equal.
∴ The given assignment problem is balanced.
Step 1.
Select the smallest element in each row and subtract this from all the elements in its row.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 4
Look for atleast one zero in each row and each column.
Here each and every row and columns having exactly one zero No need for step 2 go to step 3.

Step 3.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 5
Mark the zero by □ Mark other zeros in its column by X.
Since each row and each column contains exactly one assignment, all three machines have been assigned a job.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 6
The Optimal assignment (minimum) cost = 46

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Question 5.
A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minutes required by the experts to the application programme as follows.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 7
Assign the programmers to the programme in such a way that the total computer time is the least.
Solution:
Here the number of rows and columns are equal.
∴ The given assignment problem is balanced.
Step 1.
Select the smallest element in each row and subtract this from all the elements in its row.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 8

Step 2.
Select the smallest element in each column and subtract this from all the elements in its column.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 9

Step 3. (Assignment)
Examine the rows with exactly one zero, mark the zero by □. Mark other zeros in its column by X.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 10

Step: 4
Now examine the columns with exactly one zero marks the zero by □. Mark other zeros in its row by X.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 11
Thus all three assignments have been made. The optimal assignment schedule and total cost is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 12
The optimal assignment (minimum) cost = Rs 280

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Question 6.
A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the time man would take to perform each task is given below.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 13
How should the tasks to allocated to subordinates so as to minimize the total man-hours?
Solution:
Here the number of rows and columns are equal.
∴ The given assignment problem is balanced.
Step 1.
Select the smallest element in each row and subtract this from all the elements in its row.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 14

Step 2.
Select the smallest element in each column and subtract this from all the elements in its column.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 15

Step 3. (Assignment)
Examine the rows with exactly one zero Mark the zero by □. Mark other zeros in its row by X.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 16

Step 4.
Now examine the columns with exactly one zero. Mark the zero by □ Mark other zeros in its row by X.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 17

Step 5.
Cover all the zeros of table 4 with three lines, since three assignments were made check (✓) row S since it has no assignment.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 18

Step 6.
Develop the new revised tableau. Examine those elements that are not covered by a line in table 5. Take the smallest element. This is 1 (one) our case. By subtracting 1 from the uncovered cells.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 19
[Adding 1 to elements (Q, S, R) that line at the intersection of two lines]

Step 7.
Go to step 3 and repeat the procedure until you arrive at an optimal assignment.

Step 8.
Determine an assignment.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 20
Thus all the four assignment have been made. The optimal assignment schedule and total time is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 21
The optimum time (minimum) = 41 Hrs.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Question 7.
Find the optimal solution for the assignment problem with the following cost matrix.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 22
Solution:
Here the number of rows and columns are equal.
∴ The given assignment problem is balanced.
Step 1.
Select the smallest element in each row and subtract this from all the elements in its row.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 23

Step 2.
Select the smallest element in each column and sub tract this from all the elements in its column.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 24

Step 3. (Assignment)
Examine the rows with exactly one zero. Mark the zero by □ Mark other zeros in its column by X
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 25
Thus all the four assignments have been made. The optimal assignment schedule and total cost.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 26
The Optimum cost (minimum) = Rs 37

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Question 8.
Assign four trucks 1, 2, 3 and 4 to vacant spaces A, B, C, D, E and F so that distance travelled is minimized. The matrix below shows the distance.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 27
Solution:
Since the number of columns is less than the number of rows, the given assignment problem is unbalanced one. To balance it, introduce two dummy columns with all the entries zeros.
The revised assignment problem is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 28
Here only 4 tasks can be assigned to 4 vacant spaces.
Step 1.
It is not necessary, since each row contains zero entry. Go to step 2.

Step 2.
Select the smallest element in each column and subtract this from all the elements in its column.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 29

Step 3. (Assignment)
Since each row contains more than one zeros. Go to step 4.

Step 4.
Examine the columns with exactly one zero, mark the zero by □ Mark other zeros in its rows by X.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 30

Step 5.
Here all the four assignments have been made we can assign d1 for D then we will get d2 for E.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 31
The optimal assignment schedule and total distance is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2 32
∴ The Optimum Distant (minimum) = 12 units

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.2

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 10 Operations Research Ex 10.1 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.1

Question 1.
What is transportation problem?
Solution:
The objective of transportation problem is to determine the amount to be transported from each origin to each destinations such that the total transportation cost is minimized.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 2.
Write mathematical form of transportation problem.
Solution:
Let there be m origins and n destinations. Let the amount of supply at th i th origin is ai. Let the demand at j th destination is bj.
The cost of transporting one unit of an item from origin i to destination j is Cij and is known for all combination (i,j). Quantity transported from origin i to destination j be xij.

The objective is to determine the quantity xij to be transported over all routes (i,j) so as to minimize the total transportation cost. The supply limits at the origins and the demand requirements at the destinations must be satisfied.
The above transportation problem can be written in the following tabular form:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 1
Now the linear programming model representing the transportation problem is given by
The objective function is Minimize Z = \(\sum_{\mathbf{i}=\mathbf{1}}^{\mathbf{m}}\), \(\sum_{\mathbf{j}=\mathbf{1}}^{\mathbf{n}}\) cij xij
Subject to the constraints
\(\sum_{\mathbf{j}=\mathbf{1}}^{\mathbf{n}}\) = xij = ai, i = 1, 2 …….. m (supply constraints)
\(\sum_{\mathbf{i}=\mathbf{1}}^{\mathbf{m}}\) = xij = bj, i = 1, 2 …….. n (demand constraints)
xij ≥ 0 for all i, j (non- negative restrictions)

Question 3.
What are feasible solution and non-degenerate solutions to the transportation problem?
Solution:
Feasible Solution: A feasible solution to a transportation problem is a set of non-negative values xij (i = 1, 2,.., m, j = 1, 2, …n) that satisfies the constraints.
Non-degenerate basic feasible Solution: If a basic feasible solution to a transportation problem contains exactly m + n – 1 allocation in independent positions, it is called a Non-degenerate basic feasible solution. Here m is the number of rows and n is the number of columns in a transportation problem.

Question 4.
What do you mean by a balanced transportation problem?
Solution:
In a transportation problem if the total supply equals the total demand (Σai = Σbj) then it is said to be balanced transportation problem.

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 5.
Find an intial basic feasible solution of the following problem using north west corner rule.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 2
Solution:
Here total Supply 19 + 37 + 34 = 90
Total demand = 16 + 18 + 31 + 25 = 90
(i.e) Total supply = Total demand
∴ The given problem is balanced transportation problem
∴ we can final an initial basic feasible solution to due given problem.

From the above table we can choose the cell in the North west corner. Here the cell is (Q1, D1). Allocate as much as possible in this cell so that either the capacity of first row is exhausted or the destination requirement of the first column’s exhausted.
(i.e) x11 = min (19, 16) = 16
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 3
Now the cell in the north west corner is (O1, D2) Allocate as much as possible in the first cell so that either the capacity of second row is exhausted or the destination requirement of the first column is exhausted.
(i.e) x12 = min (3, 18) = 3
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 4
Reduced transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 5
Now the cell in the north west corner is (O2, D2)
x22 = min (37, 15) = 15
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 6
Now the cell in the north west corner is (O2, D3)
x23 = min (22, 31) = 9
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 7
Now the cell in the north west corner is (O3, D3)
x33 = min (34, 9) = 9
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 8
Thus we have the following allocations
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 9
Transportation schedule:
O1 → D1, O1, → D2, O2 → D2; O2 → D3 O3 → D3; O3 → D4
= (16 × 5) + (3 × 3) + (15 × 7) + (22 × 9) + (9 × 7) + (25 × 5)
= 80 + 9 + 105 + 198 + 63 + 125
= 580

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 6.
Determine an intial basic feasible solution of the following transportation problem by north west corner method.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 10
Solution:
Here total capacity (ai) = 30 + 40 + 50 = 120
Total demand (bj) = 35 + 28 + 32 + 25 = 120
(i.e) Total capacity = Total demand
∴ The given problem is balanced transportation.
∴ We can find an initial basic feasible solution to the given problem.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 11
From the above table we can choose the cell in the North west corner. Here the cell is (chennai, Bangalore)
x11 = min (30, 35) = 30
Reduced transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 12
Now the cell in the North west corner is (Madurai, Bangalore)
x21 = min(40, 5) = 5
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 13
From the above table we can choose the cell in the North west corner. Here the cell is (Nasik, Madurai)
x22 = min (35, 28) = 28
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 14
From the above table we can choose the cell in the North west corner. Here the cell is (Bhopal, Madurai)
x22 = min (7, 32) = 7
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 15
From the above table we can choose the cell in the North west corner. Here the cell is (Trichy, Bhopal)
x33 = min (50, 25) = 25
Reduced transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 16
x34 = min (25, 25) = 25
Thus we have the following allocations
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 17
Transportation Schedule:
Chennai → Bangalore; Madurai → Bangalore;
Madurai → Naisk; Madurai → Bhopal
Trichy → Bhopal; Trichy → Delhi
The total transportation cost =
(30 × 6) + (5 × 5) + (28 × 11) + (7 × 9) + (25 × 7) + (25 × 13)
= 180 + 25 + 308 + 63 + 175 + 325
= 1076

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 7.
Obtain an initial basic feasible solution to the following transportation problem by using least-cost method.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 18
Solution:
The given transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 19
Total supply = 25 + 35 + 40 = 100
Total demand = 30 + 25 + 45 = 100
(i.e) Total supply = Total demand
∴ The given problem is a balanced transportation problem.
Hence there exists a feasible solution to the given problem.
The least cos is 4 corresponds to the cell (O2, D3)
Allocate min (35, 45) = 35 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 20
The least cost corresponds to the cell (O1, D3)
Allocate min (25, 10) = 10 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 21
The least cost is 6 corresponds to the cell (O3, D2)
Allocate min (40, 25) = 25 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 22
The least cost is 7 corresponds to the cell (O3, D1)
Allocate min (15, 30) = 15
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 23
Thus we have the following allocations
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 24
Transportation Schedule:
O1 → D1; O1, → D3; O2 → D3; O3 → DI; O3 → D2
Total Transportation cost
= (15 × 9) + (10 × 5) + (35 × 4) + (15 × 7) + (25 × 6)
= 135 + 50 + 140 + 105 + 150
= 580

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 8.
Explain vogel’s approximation method by obtaining initial feasible solution of the following transportation problem.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 25
Solution:
Here Σ ai = 6 + 1 + 10 = 17
Σ bj = 7 + 5 + 3 + 2 = 17
Σ ai = Σ bj
(i.e) Total supply = Total Demand
∴ The given problem is balanced transportation problem
Hence there exists a feasible solution to the given problem.
First let us find the difference (penalty) between the first two smallest costs in each row and column and write them in brackets against the respective rows and columns.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 26
Choose the largest difference. Here the largest difference is 6 which corresponds to column D4
In this column choose the least cost. Here the least cost corresponds to (O2, D4)
Allocate min (1, 2) = 1 unit to this cell the reduced transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 27
choose the largest difference 5 which corresponds to column D2. Here the least cost corresponds to (O1, D2).
Allocate min (6, 5) = 5 units in this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 28
Choose the largest difference 5 which corresponds to row O1. Here the least cost corresponds to (O1, D1)
Allocate min (1, 7) = 1 unit in this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 29
Choose the largest difference 4 which corresponds to row O3. Here least cost corresponds to (10, 6) = 6 units in this cell.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 30
Choose the largest difference 6 which corresponds to row O3. Here the least cost corresponds to (O3, D4).
Allocate min (4, 1) = 1
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 31
Thus we have the following allocations
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 32
Transportation schedule
O1 → D1; O1 → D2; O2 → D4;
O3 → D1; O3 → D3; O3 → D4
Total transportation cost:
= (1 × 2) + (5 × 3) + (1 × 1) + (6 × 5) + (3 × 15) + (1 × 9)
= 2 + 15 + 1 + 30 + 45 + 9
= 102

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 9.
Consider the following transportation problem.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 33
Determine initital basic feasible solution by VAM
Solution:
Given Transportation problem is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 34
Here Σ ai = Σ bj = 100
∴ The given problem is balanced transportation problem.
Hence there exists a feasible solution to the given problem.
First let us find the difference (penalty) between the first two smallest costs in each row and column and write them in brackets against the respective rows and columns
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 35
Choose the largest difference. Here the difference is 3 which corresponds to D2
In this column choose the least cost. Here the least cos corresponds to (O3, D2)
Allocate min (20, 40) = 20 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 36
Choose the largest difference is 4 which corresponds to column D3. In this column choose the least cost. Here the least cost corresponds to (O1, D3).
Allocate min (30, 20) = 20 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 37
Choose the largest different is 3 which corresponds to column D2. In this column choose the least cost. Here the least cost corresponds to (O2, D2)
Allocate min (50, 20) = 20 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 38
Choose the largest difference is 2 which corresponds to column D4. In this column choose the least cost. Here the least cost corresponds to (O2, D4).
Allocate min (30, 10) = 10 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 39
Allocate min (20, 30) = 20 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 40
Here
x11 = 10
x13 = 20
x21 = 20
x22 = 20
x24 = 10
x32 = 20
Transportation schedule
O1 → D1; O1 → D3; O2 → D1;
O2 → D2; O2 → D4; O3 → D2
The transportation cost
= (10 × 5) + (20 × 3) + (20 × 4) + (20 × 5) + (10 × 4) + (20 × 2)
= 50 + 60 + 80 + 100 + 40 + 40
= 370

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 10.
Determine basic feasible solution to the following transportation problem using North west Corner rule.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 41
Solution:
Here total supply = 4 + 8 + 9 = 21
Total demand = 3 + 3 + 4 + 5+ 6 = 21
(i.e) Total supply = Total demand
∴ The given problem is balanced transportation problem.
∴ we can find an initial basic feasible solution to the given problem.
From the above table we can choose the cell in the North west corner. Here the cell is (P, A)
Allocate as much as possible in this cell so that either the capacity of first row is exhausted or the destination requirement of the first column is exhausted.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 42
Form the above table we can choose the cell in North west corner. Here the cell is (P,B)
x = min (1, 3) = 1
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 43
From the above table we can choose the cell in north west corner. Here the cell is (Q, B)
x = min (2, 8) = 2
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 44
From the above table, we can choose the cell in North west corner. Here the cell is (Q, C)
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 45
From the above table, we can choose the cell in North west corner. Here the cell is (Q, D)
x = min (2, 5) = 2
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 46
From the above table, we can choose the cell in North west corner. Here the cell is (R, D)
x = min (9, 3) = 3
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 47
Thus we have the following table
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 48
Transportation Schedule:
P → A; P → B; Q → B; Q → C; Q → D R → D; R → E
Total transportation cost:
= (3 × 2) + (1 × 11) + (2 × 4) + (4 × 7) + (2 × 2) + (3 × 8) + (6 × 2)
= 6 + 11 + 8 + 28 + 4 + 24 + 72
= 153

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 11.
Find the initial basic feasible solution of the following transportation problem:
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 49
Using
(i) North West corner tule
(ii) Least Cost method
(iii) Vogel’s approximation method
Solution:
(i) North west corner rule:
Here the total supply = 10 + 10 + 10 = 30
Total demand = 7 + 12 + 11 = 30
(i.e) Total supply = Total demand
The given problem is balanced transportation problem.
∴ we can find an initial basic feasible solution to the given problem.
From the above table we can choose the cell in the North west corner. Here the cell is (A, I)
x11 = min (7, 10) = 7
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 50
From the above table we can choose the cell in the north west corner. Here the cell is (B, I)
x = min (3, 12) = 3
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 51
From the above table we can choose the cell in the North west corner. Here the cell is (B, II)
x = min (9, 10) = 9
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 52
Here the cell in the North west corner is (C, II)
x = min (11, 1) = 1
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 53
Thus we have the following allocations
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 54
Transportation schedule:
A → I; B → I; B → II; C → II; C → III
Total transportation cost:
= (7 × 1) + (3 × 0) + (9 × 4) + (1 × 1) + (10 × 5)
= 7 + 0 + 36 + 1 + 50
= 94

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

(ii) Least cost method:
The given transportation table is
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 55
Here Total supply = Total demand = 30
∴ The given problem is a balanced transportation problem.
Hence there exists a feasible solution to the given problem.
The least cost is 0 corresponds to the cell (B, I)
Allocate min (12, 10) = 10 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 56
The least cost 1 corresponds to the cell (C, II)
Allocate min (11, 10) = 10 units to this cell
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 57
Here the least cost 2 corresponds to the cell (B, III)
Allocate min (2, 10) = 2 units to this cell.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 58
Here the least cost is 5 corresponds to the cell (C, III)
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 59
Transportation schedule:
A → III; B → I; B → III; C → II; C → III
Total transportation cost:
= (7 × 6) + (10 × 10) + (2 × 2) + (10 × 1) + (1 × 5)
= 42 + 0 + 4 + 10 + 5
= 61

(iii) Vogel’s approximation method:
Here Σ ai = Σ bj = 30
(i.e) Total supply = Total demand
∴ This given problem is balanced transportation problem.
Hence there exists a feasible solution to the given problem.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 60
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 61
A → I; B → I; B → III; C → I; C → II
Total transportation cost:
= (7 × 1) + (2 × 0) + (10 × 2) + (1 × 3) + (10 × 1)
= 7 + 0 + 20 + 3 + 10
= 40

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Question 12.
Obtain an initial basic feasible solution to the following transportation problem by north west corner method.
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 62
Solution:
Here the total available = 250 + 300 + 400 = 950
Total Required = 200 + 225 + 275 + 250 = 950
(i.e) Total Available = total required
∴ The given problem is balanced transportation problem.
we can find an initial basic feasible solution to the given problem.
From the above table, we can choose the cell in the North west corner. Here the cell is (A, D).
x11 = min (250, 200) = 200
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 63
From the above table we can choose the cell in North west corner. Here the cell is (A, E)
x = min (50, 225) = 50
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 64
From the above table, the north west corner cell is (B, E)
x = min (300, 175) = 175
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 65
From the above table, the north west corner cell is (B, F)
x = min (125, 275) = 125
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 66
Here the north west corner cell is (C, F)
x = min (400, 150) = 150
Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1 67
Transportation schedule:
A → D; A → E; B → E; B → F; C → G
Total Transportation cost:
= (200 × 11) + (50 × 13) + (175 × 18) + (125 × 14) + (150 × 13) + (250 × 10)
= 2200 + 650 + 3150 + 1750 + 1950 + 2500
= 12,200

Samacheer Kalvi 12th Business Maths Guide Chapter 10 Operations Research Ex 10.1

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 9 Applied Statistics Miscellaneous Problems Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 9 Applied Statistics Miscellaneous Problems

Question 1.
Using three yearly moving averages, Determine the trend values from the following data.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 1
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 2

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems

Question 2.
From the following data, calculate the trend values using fourly moving averages.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 3
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 4

Question 3.
Fit a straight line trend by the method of least squares to the following data.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 5
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 6
Therefore, the required equation of the straight line trend is given by
y = a + bx
y = 55.9875 + 0.830 x
⇒ y = 55.9875 + 0.83 (\(\frac { x-1983.5 }{0.5}\))
The trend values can be obtained by
When x = 1980
y = 55.9875 + 0.83 (\(\frac { 1980-1983.5 }{0.5}\))
= 55.9875 + 0.83 (-7)
= 55.9875 – 5.81
= 50.1775
When x = 1981
y = 55.9875 + 0.83 (\(\frac { 1981-1983.5 }{0.5}\))
= 55.9875 + 0.83 (-5)
= 55.9875 – 4.15
= 51.8375
When x = 1982
y = 55.9875 + 0.83 (\(\frac { 1981-1983.5 }{0.5}\))
= 55.9875 + 0.83 (-3)
= 55.9875 – 2.49
= 53.4975
When x = 1983
y = 55.9875 + 0.83 (\(\frac { 1983-1983.5 }{0.5}\))
= 55.9875 + 0.83 (-1)
= 55.9875 – 0.83
= 55.1575
When x = 1984
y = 55.9875 + 0.83 (\(\frac { 1984-1983.5 }{0.5}\))
55.9875 + 0.83 (1)
= 56.8175
when x = 1985
y = 55.9875 + 0.83 (\(\frac { 1985-1983.5 }{0.5}\))
= 55.9875 + 0.83 (3)
= 55.9875 + 2.49
= 58.4775
when x = 1986
y = 55.9875 + 0.83 (\(\frac { 1986-1983.5 }{0.5}\))
= 55.9875 + 0.83 (5)
= 55.9875 + 4.15
= 60.1375
when x = 1987
y = 55.9875 + 0.83 (\(\frac { 1987-1983.5 }{0.5}\))
= 55.9875 + 0.83 (7)
= 55.9875 + 5.81
= 61.7975

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems

Question 4.
Fit a straight line trend by the method of least squares to the following data.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 7
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 8
Lasperyre’s price Index number
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 9
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 10
Hence Fisher’s Ideal Index satisfies Time reversal test

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems

Question 5.
Using the following data, construct Fisher’s Ideal Index Number and Show that it satisfies Factor Reversal Test and Time Reversal Test?
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 11
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 12
Factor reversal test
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 13
Hence Fisher’s Ideal Index satisfies Factor reversal test.

Question 6.
Compute the consumer price index for 2015 on the basis of 2014 from the following data.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 14
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 15

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems

Question 7.
An Enquiry was made into the budgets of the middle class families in a city gave the following information.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 16
What changes in the cost of living have taken place in the middle class families of a city?
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 17
Conclusion:
The cost of living has increased up to 26.10% in 2011 as compared to 2010.

Question 8.
From the following data, calculate the control limits for the mean and range chart.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 18
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 19
UCL = \(\bar { \bar x}\) + A2\(\bar { R}\)
= 51 + 0.577(6.5)
= 51 + 3.7505
= 54.7505
= 54.75
CL = \(\bar { \bar x}\) = 51
UCL = \(\bar { \bar x}\) – A2\(\bar { R}\)
= 51 – 0.577(6.5)
= 51 – 3.7505
= 47.2495
= 47.25
The control limits for Range chart is
UCL = D4\(\bar { R}\)
= 2.114(6.5)
= 13.741
CL = \(\bar { R}\) = 6.5
LCL = D3\(\bar { R}\) = 0(6.5) = 0

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems

Question 9.
The following data gives the average life(in hours) and range of 12 samples of 5 lamps each. The data are
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 20
Construct control charts for mean and range Comment on the control limits.
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 21
UCL = \(\bar { \bar x}\) + A2\(\bar { R}\)
= 1367.5 + 0.577(427.5)
= 1367.5 + 246.6675
= 1614.1675
= 1614.17
CL = \(\bar { \bar x}\) = 1367.5
LCL = \(\bar { \bar x}\) + A2\(\bar { R}\)
= 1367.5 – 0.577(427.5)
= 1367.5 – 246.6675
= 1120.8325
= 1120.83
The control limits for Range chart is
UCL = D4\(\bar { R}\)
= 2.115(427.5)
= 904.1625
= 904.16
CL = \(\bar { R}\) = 427.5
LCL = D3\(\bar { R}\)
= 0(427.5)
= 0

Question 10.
The following are the sample means and I ranges for 10 samples, each of size 5. Calculate ; the control limits for the mean chart and range chart and state whether the process is in control or not.
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 22
Solution:
Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems 23
UCL = \(\bar { \bar x}\) + A2\(\bar { R}\)
= 4.982 + 0.577(0.36)
= 4.982 + 0.20772
= 5.18972
= 5.19
CL = \(\bar { \bar x}\) = 4.982
LCL = \(\bar { \bar x}\) + A2\(\bar { R}\)
= 4.982 – 0.577(0.36)
= 4.982 – 0.20772
= 4.77428
= 4.774
The control limits for range chart is
UCL = D2\(\bar { R}\) = 2.115(3.6)
= 7.614
CL = \(\bar { R}\) = 3.6
LCL = D3\(\bar { R}\)
= 0(0.36) = 0

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Miscellaneous Problems

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Ex 9.4

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Business Maths Guide Pdf Chapter 9 Applied Statistics Ex 9.4 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 9 Applied Statistics Ex 9.4

Question 1.
A time series is a set of data recorded
(a) Periodically
(b) Weekly
(c) successive points of time
(d) all the above
Solution:
(d) all the above

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Ex 9.4

Question 2.
A time series consists of
(a) Five components
(b) Four components
(c) Three components
(d) Two components
Solution:
(b) Four components

Question 3.
The components of a time series which is attached to short term fluctuation is
(a) Secular trend
(b) Seasonal variations
(c) Cyclic variation
(d) Irregular variation
Solution:
(d) Irregular variation

Question 4.
Factors responsible for seasonal variations are
(a) Weather
(b) Festivals
(c) Social customs
(d) All the above
Solution:
(d) All the above

Question 5.
The additive model of the time series with the components T, S, C and I is
(a) y = T + S + C × I
(b) y = T + S × C × I
(c) y = T + S + C + I
(d) y = T + S × C + I
Solution:
(c) y = T + S + C + I

Question 6.
Least square method of fitting a trend is
(a) Most exact
(b) Least exact
(c) Full of subjectivity
(d) Mathematically unsolved
Solution:
(a) Most exact

Question 7.
The value of ‘b’ in the trend line y = a + bx is
(a) Always positive
(b) Always negative
(c) Either positive or negative
(d) Zero
Solution:
(c) Either positive or negative

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Ex 9.4

Question 8.
The component of a time series attached to long term variation is trended as
(a) Cyclic variation
(b) Secular variations
(c) Irregular variation
(d) Seasonal variations
Solution:
(b) Secular variations

Question 9.
The seasonal variation means the variations occurring with in
(a) A number of years
(b) within a year
(c) within a month
(d) within a week
Solution:
(b) within a year

Question 10.
Another name of consumer’s price index number is:
(a) Whole-sale price index number
(b) Cost of living index
(c) Sensitive
(d) Composite
Solution:
(b) Cost of living index

Question 11.
Cost of living at two different cities can be compared with the help of
(a) Consumer price index
(b) Value index
(c) Volume index
(d) Un-weighted index
Solution:
(a) Consumer price index

Question 12.
Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:
(a) 110
(b)108
(c) 100
(d) 109
Solution:
(d) 109
Hint:
01 = 110; pp01 = 108
Fisher’s Ideal Index = \(\sqrt { 110×108 }\) = \(\sqrt { 11880 }\) = 108.99 = 109

Question 13.
Most commonly used index number is:
(a) Volume index number
(b) Value index number
(c) Price index number
(d) Simple index number
Solution:
(c) Price index number

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Ex 9.4

Question 14.
Consumer price index are obtained by:
(a) Paasche’s formula
(b) Fisher’s ideal formula
(c) Marshall Edgeworth formula
(d) Family budget method formula
Solution:
(d) Family budget method formula

Question 15.
Which of the following Index number satisfy the time reversal test?
(a) Laspeyre’s Index number
(b) Paasche’s Index number
(c) Fisher Index number
(d) All of them.
Solution:
(c) Fisher Index number

Question 16.
While computing a weighted index, the current period quantities are used in the:
(a) Laspeyre’s method
(b) Paasche’s method
(c) Marshall Edgeworth method
(d) Fisher’s ideal method
Solution:
(b) Paasche’s method

Question 17.
The quantities that can be numerically measured can be plotted on a
(a) p – chart
(b) c – chart
(c) x bar chart
(d) np – chart
Solution:
(c) x bar chart

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Ex 9.4

Question 18.
How many causes of variation will affect the quality of a product?
(a) 4
(b) 3
(c) 2
(d) 1
Solution:
(c) 2

Question 19.
Variations due to natural disorder is known as
(a) random cause
(b) non-random cause
(c) human cause
(d) all of them
Solution:
(a) random cause

Question 20.
The assignable causes can occur due to
(a) poor raw materials
(b) unskilled labour
(c) faulty machines
(d) all of them
Solution:
(d) all of them

Question 21.
A typical control charts consists of
(a) CL, UCL
(b) CL, LCL
(c) CL, LCL, UCL
(d) UCL, LCL
Solution:
(c) CL, LCL, UCL

Question 22.
\(\bar { x}\) chart is a
(a) attribute control chart
(b) variable control chart
(c) neither Attribute nor variable control chart
(d) both Attribute and variable control chart
Solution:
(b) variable control chart

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Ex 9.4

Question 23.
R is calculated using
(a) xmax – xmin
(b) xmin – xmax
(c) \(\bar { x}\)max – \(\bar { x}\)min
(d) \(\bar {\bar x}\)max – \(\bar {\bar x}\)min
Solution:
(a) xmax – xmin

Question 24.
The upper control limit for x chart is given by
(a) \(\bar { x}\) + A2\(\bar { R}\)
(b) \(\bar {\bar x}\) + A2R
(c) \(\bar {\bar x}\) + A2\(\bar { R}\)
(d) \(\bar { x}\) + A2\(\bar {\bar R}\)
Solution:
(c) \(\bar {\bar x}\) + A2\(\bar { R}\)

Question 25.
The LCL for R chart is given by
(a) D2\(\bar { x}\)
(b) D2\(\bar {\bar R}\)
(c) D3\(\bar {\bar R}\)
(d) D3\(\bar { x}\)
Solution:
(d) D3\(\bar { x}\)

Samacheer Kalvi 12th Business Maths Guide Chapter 9 Applied Statistics Ex 9.4