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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Construct Fisher’s price index for the data below:

Commodity

Price 2013

Price 2014

Quantity 2013

Quantity 2014

A

6

10

50

56

B

2

2

100

120

C

4

6

60

60

D

10

12

30

24

E

8

12

40

36
Options:

141.31

132.09

139.78

135.58

Correct Answer:

139.78

Explanation:

The correct answer is Option (3) → 139.78

Commodity

$p_0$​

$q_0$​

$p_1$​

$q_1$​

$p_0​q_0$​

$p_1​q_0$​

$p_0​q_1$​

$p_1​q_1$​

A

6

50

10

56

300

500

336

560

B

2

100

2

120

200

200

240

240

C

4

60

6

60

240

360

240

360

D

10

30

12

24

300

360

240

288

E

8

40

12

36

320

480

288

432

Total

 

 

 

 

$\sum p_0q_0 = 1360$

$\sum p_1q_0 = 1900$

$\sum p_0q_1 = 1344$

$\sum p_1q_1 = 1880$

Fisher's Index Number:

$P_{01} = \sqrt{\frac{\sum p_1q_0}{\sum p_0q_0} \times \frac{\sum p_1q_1}{\sum p_0q_1}} \times 100 = \sqrt{\frac{1900}{1360} \times \frac{1880}{1344}} \times 100$

$= \sqrt{1.397 \times 1.398} \times 100 = 139.78$

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