Balbharati Maharashtra State Board 12th Commerce Maths Solution Book Pdf Chapter 5 Index Numbers Miscellaneous Exercise 5 Questions and Answers.

## Maharashtra State Board 12th Commerce Maths Solutions Chapter 5 Index Numbers Miscellaneous Exercise 5

(I) Choose the correct alternative.

Question 1.

Price Index Number by Simple Aggregate method is given by

Answer:

(c) \(\frac{\sum p_{1}}{\sum p_{0}} \times 100\)

Question 2.

Quantity Index Number by Simple Aggregate Method is given by

Answer:

(c) \(\frac{\sum q_{1}}{\sum q_{0}} \times 100\)

Question 3.

Value Index Number by Simple Aggregate Method is given by

Answer:

(b) \(\sum \frac{p_{0} q_{1}}{p_{0} q_{0}} \times 100\)

Question 4.

Price Index Number by Weighted Aggregate Method is given by

Answer:

(c) \(\frac{\sum p_{1} w}{\sum p_{0} w} \times 100\)

Question 5.

Quantity Index Number By Weighted Aggregate Method is given by

Answer:

(c) \(\frac{\sum q_{1} w}{\sum q_{0} w} \times 100\)

Question 6.

Value Index Number by Weighted aggregate Method is given by

Answer:

(d) \(\frac{\sum p_{1} q_{1} w}{\sum p_{0} q_{0} w} \times 100\)

Question 7.

Laspeyre’s Price Index Number is given by

Answer:

(c) \(\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100\)

Question 8.

Paassche’s Price Index Number is given by

Answer:

(d) \(\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100\)

Question 9.

Dorbish-Bowley’s Price Index Number is given by

Answer:

(c) \(\frac{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}}+\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}}}{2} \times 100\)

Question 10.

Fisher’s Price Number is given by

Answer:

(a) \(\sqrt{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times \frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}}} \times 100\)

Question 11.

Marshall-Edge worth’s Price Index Number is given by

Answer:

(a) \(\frac{\sum p_{1}\left(q_{0}+q_{1}\right)}{\sum p_{0}\left(q_{0}+q_{1}\right)} \times 100\)

Question 12.

Walsh’s Price Index Number is given by

Answer:

(a) \(\frac{\sum p_{1} \sqrt{q_{0} q_{1}}}{\sum p_{0} \sqrt{q_{0} q_{1}}} \times 100\)

Question 13.

The Cost of Living Index Number using Aggregate Expenditure Method is given by

Answer:

(a) \(\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100\)

Question 14.

The Cost of Living Index Number using Weighted Relative Method is given by

Answer:

(a) \(\frac{\sum \mathrm{IW}}{\sum \mathrm{W}}\)

(II) Fill in the blanks.

Question 1.

Price Index Number by Simple Aggregate Method is given by ____________

Answer:

\(\frac{\sum p_{1}}{\sum p_{0}} \times 100\)

Question 2.

Quantity Index number by Simple Aggregate Method is given by ____________

Answer:

\(\frac{\sum q_{1}}{\sum q_{0}} \times 100\)

Question 3.

Value Index Number by Simple Aggregate Method is given by ____________

Answer:

\(\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{0}} \times 100\)

Question 4.

Price Index Number by Weighted Aggregate Method is given by ____________

Answer:

\(\frac{\sum p_{1} w}{\sum p_{0} w} \times 100\)

Question 5.

Quantity Index Number by Weighted Aggregate Method is given by ____________

Answer:

\(\frac{\sum q_{1} w}{\sum q_{0} w} \times 100\)

Question 6.

Value Index Number by Weighted Aggregate Method is given by ____________

Answer:

\(\frac{\sum p_{1} q_{1} w}{\sum p_{0} q_{0} w} \times 100\)

Question 7.

Laspeyre’s Price Index Number is given by ____________

Answer:

\(\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100\)

Question 8.

Paasche’s Price Index Number is given by ____________

Answer:

\(\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100\)

Question 9.

Dorbish-Bowley’s Price Index Number is given by ____________

Answer:

\(\frac{1}{2}\left[\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}}+\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}}\right] \times 100\)

Question 10.

Fisher’s Price Index Number is given by ____________

Answer:

\(\sqrt{\left[\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times \frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}}\right]} \times 100\)

Question 11.

Marshall-Edgeworth’s Price Index Number is given my ____________

Answer:

\(\frac{\sum p_{1}\left(q_{0}+q_{1}\right)}{\sum p_{0}\left(q_{0}+q_{1}\right)} \times 100\)

Question 12.

Walsh’s Price Index Number is given by ____________

Answer:

\(\frac{\sum p_{1} \sqrt{q_{0} q_{1}}}{\sum p_{0} \sqrt{q_{0} q_{1}}} \times 100\)

(III) State whether each of the following is True or False.

Question 1

\(\frac{\sum p_{1}}{\sum p_{0}} \times 100\) is the Price Index Number by Simple Aggregate Method.

Answer:

True

Question 2

\(\frac{\sum q_{0}}{\sum q_{1}} \times 100\) is the Quantity Index Number by Simple Aggregate Method.

Answer:

False

Question 3.

\(\sum \frac{p_{0} q_{0}}{p_{1} q_{1}} \times 100\) is value Index Number by Simple Aggregate Method.

Answer:

False

Question 4.

\(\sum \frac{p_{1} q_{0}}{p_{1} q_{1}} \times 100\) Paasche’s Price Index Number.

Answer:

False

Question 5.

\(\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100\) is Laspeyre’s Price Index Number.

Answer:

False

Question 6.

\(\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times \frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}} \times 100\) is Dorbish-Bowley’s Index Number.

Answer:

False

Question 7.

\(\frac{1}{2}\left[\sqrt{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}}}+\frac{\sqrt{p_{1} q_{1}}}{\sqrt{p_{0} q_{1}}}\right] \times 100\) is Fisher’s Price Index Number.

Answer:

False

Question 8.

\(\frac{\sum p_{0}\left(q_{0}+q_{1}\right)}{\sum p_{1}\left(q_{0}+q_{1}\right)} \times 100\) is Marshall-Edgeworth’s Index Number.

Answer:

False

Question 9.

\(\frac{\sum p_{0} \sqrt{q_{0} q_{1}}}{\sum p_{1} \sqrt{q_{0} q_{1}}} \times 100\) is Walsh’s Price Index Number.

Answer:

False

Question 10.

\(\sqrt{\frac{\sum p_{1} q_{0}}{\sum p_{0} q_{0}}} \times \sqrt{\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}}} \times 100\) is Fisher’s Price Index Number.

Answer:

True

(IV) Solve the following problems.

Question 1.

Find the price Index Number using simple Aggregate Method Consider 1980 as base year.

Solution:

Question 2.

Find the Quantity Index Number using Simple Aggregate Method.

Solution:

Question 3.

Find the Value Index Number using Simple Aggregate Method.

Solution:

= \(\frac{10200}{8400}\) × 100

= 121.43

Question 4.

Find x if the Price Index Number using Simple Aggregate Method is 200.

Solution:

Question 5.

Calculate Laspeyre’s and Paasche’s Price Index Number for the following data.

Solution:

Question 6.

Calculate Dorbish-Bowley’s Price Index Number for the following data.

Solution:

Question 7.

Calculate Marshall-Edge worth’s Price Index Number for the following data.

Solution:

Question 8.

Calculate Walsh’s Price Index Number for the following data.

Solution:

Question 9.

Calculate Laspeyre’s Price Index Number for the following data.

Solution:

Question 10.

Find x if Laseyre’s Price Index Number is same as Paasche’s Price Index Number for the following data.

Solution:

Question 11.

Find x if Walsh’s Price Index Number is 150 for the following data.

Solution:

Question 12.

Find x if Paasche’s Price Index Number is 140 for the following data.

Solution:

Question 13.

Given that Laspeyre’s and Paasche’s Index Number are 25 and 16 respectively. Find Dorbish-Bowley’s and Fisher’s Price Index Number.

Solution:

= \(\sqrt{25 \times 16}\)

= 20

Question 14.

If Laspeyre’s and Dorbish Price Index Number are 150.2 and 152.8 respectively, find Paasche’s rice Index Number.

Solution:

Question 15.

If Σp_{0}q_{0} = 120, Σp_{0}q_{1} = 160, Σp_{1}q_{1} = 140, and Σp_{1}q_{0} = 200 find Laspeyre’s, Paasche’s, Dorbish-Bowley’s, and Marshall-Edgeworth’s Price Index Numbers.

Solution:

Question 16.

Given that Σp_{0}q_{0} = 130, Σp_{1}q_{1} = 140, Σp_{0}q_{1} = 160, and Σp_{1}q_{0} = 200, find Laspeyare’s, Passche’s, Dorbish-Bowely’s and Mashall-Edegeworth’s Price Inbox Numbers.

Solution:

Question 17.

Given that Σp_{1}q_{1} = 300, Σp_{0}q_{1} = 140, Σp_{0}q_{0} = 120, and Marshall-Edegeworth’s Price Inbox Number is 120, find Laspeyre’s Price Index Number.

Solution:

p_{01}(P) = \(\frac{\sum p_{1} q_{1}}{\sum p_{0} q_{1}} \times 100\)

= \(\frac{300}{320}\) × 100

= 93.75

Question 18.

Calculate the cost of living number for the following data.

Solution:

Question 19.

Find the cost living index number by the weighted aggregate method.

Solution:

Question 20.

Find the cost of living index number by Family Budget Method for the following data. Also, find the expenditure of a person in the year 2008 if his expenditure in the year 2005 was ₹ 10,000.

Solution:

Question 21.

Find x if cost of living index number is 193 for the following data.

Solution:

Question 22.

The cost of living numbers for years 2000 and 2003 are 150 and 210 respectively. A person earns ₹ 13,500 per month in the year 2000. What should be his monthly earnings in the year 2003 in order to maintain the same standard of living?

Solution:

CLI (2000) = 150

CLI (2003) = 210

Income (2000) = 13500

Income (2003) = ?

Real Income = \(\frac{\text { Income }}{\mathrm{CLI}} \times 100\)

For 2000, Real Income = \(\frac{13500}{150} \times 100\) = ₹ 9000

For 2003, Real Income = \(\frac{\text { Income }}{\mathrm{CLI}} \times 100\)

∴ 9000 = \(\frac{\text { Income }}{210} \times 100\)

∴ Income = \(\frac{9000 \times 210}{100}\) = 18900

∴ Income in 2003 = ₹ 18900