Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Compute Fisher's Ideal Index No.

Commodities

Price (₹)

Value

Price (₹)

Value

 

2008

2010

A

5

40

8

40

B

8

64

12

168

C

10

120

22

132

D

12

144

26

208

E

16

288

20

300

Options:

194.51

191.52

190.81

189.77

Correct Answer:

190.81

Explanation:

The correct answer is Option (3) → 190.81

For calculating base period and current period quantity we divide value by price.

 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

5

8

8

5

64

40

40

25

B

8

8

12

14

96

64

168

112

C

10

12

22

6

264

120

132

60

D

12

12

26

8

312

144

208

96

E

16

18

30

10

540

288

300

160

 

 

 

 

 

$\sum p_1​q_0= 1276$

$\sum p_0​q_0= 656$

$\sum p_1​q_1= 848$

$\sum p_0​q_1= 453$

Fisher's Method:

$P_{01} = \sqrt{\frac{\sum p_1q_0}{\sum p_0q_0} \times \frac{\sum p_1q_1}{\sum p_0q_1}} \times 100 = \sqrt{\frac{1276}{656} \times \frac{848}{453}} \times 100$

$= \sqrt{\frac{1082048}{297168}} \times 100$

$= \sqrt{3.641} \times 100 = 190.81$