Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Using the following data, compute Fisher's Ideal Quantity Index Numbers for the current year:

Commodity

Base Year

Current Year

Price

Qty. 

Price

 Qty.

(₹)

(Kg.)

(₹)

(Kg.)

A

12

20

15

25

B

10

08

16

10

C

15

02

12

01

D

60

01

65

01

E

03

02

10

01

Options:

122.32

125.65

115.36

119.69

Correct Answer:

115.36

Explanation:

The correct answer is Option (3) → 115.36

Commodity

$p_0$​

$q_0$​

$p_1$​

$q_1$​

$p_1​q_0$​

$p_0​q_0$​

$p_1​q_1$​

$p_0​q_1$​

A

12

20

15

25

300

240

375

300

B

10

08

16

10

128

80

160

100

C

15

02

12

01

24

30

12

15

D

60

01

65

01

65

60

65

60

E

03

02

10

01

20

06

10

03

Total

 

 

 

 

$\sum p_1q_0 = 537$

$\sum p_0q_0 = 416$

$\sum p_1q_1 = 622$

$\sum p_0q_1 = 478$

Fisher's Quantity Index Number ($Q_{01}$):

$Q_{01} = \sqrt{\frac{\sum q_1p_0}{\sum q_0p_0} \times \frac{\sum q_1p_1}{\sum q_0p_1}} \times 100$

$Q_{01} = \sqrt{\frac{478}{416} \times \frac{622}{537}} \times 100 \approx 115.36$