Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

From the data given below construct a price index number of the group of four commodities using the appropriate formula:

Commodity

Base Year (2014)

Price

Base Year (2014)

Expenditure

Current Year (2015)

Price

Current Year (2015)

Expenditure

A

2

40

5

75

B

4

16

8

40

C

1

10

2

24

D

5

25

10

60

Options:

317.27

219.12

223.17

230.15

Correct Answer:

219.12

Explanation:

The correct answer is Option (2) → 219.12

However, expenditure is given which is the product of price and quantity. To find out quantity total expenditure will be divided by the price per unit.

Commodity

Items

$p_0$​

$q_0$​

$p_1$​

$q_1$​

$p_0​q_0$​

$p_0​q_1$​

$p_1​q_1$​

$p_1​q_0$​

A

1

2

20

5

15

40

30

75

100

B

2

4

4

8

5

16

20

40

32

C

3

1

10

2

12

10

12

24

20

D

4

5

5

10

6

25

30

60

50

1

1

1

1

1

1

$\sum p_0q_0 = 91$

$\sum p_0q_1 = 92$

$\sum p_1q_1 = 199$

$\sum p_1q_0 = 202$

Since Fisher's formula is ideal formula, so we calculate price index number by Fisher's Method.

$\text{Fisher's index number } P_{01} = \sqrt{\frac{\sum p_1q_0}{\sum p_0q_0} \times \frac{\sum p_1q_1}{\sum p_0q_1}} \times 100$

$P_{01} = \sqrt{\frac{202}{91} \times \frac{199}{92}} \times 100$

$P_{01} = \sqrt{4.8015} \times 100 = 2.1912 \times 100 = 219.12$