Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Following table shows the data on energy consumption and expenditure at Badarpur Thermal Power Station, in Delhi region. Construct an aggregative price index for the energy expenditures in year 2015 using Laspeyres’ index.

Sector

Quantity (weights)

Unit Price (₹/kWh)

 

Year 1987

Year 2015

Year 1987

Year 2015

Commercial

5416

6015

1.97

10.92

Residential

15293

20262

2.32

6.16

Industrial

21287

17832

0.79

5.13

Agriculture

9473

8804

2.25

8.10

Options:

385

403

415

422

Correct Answer:

403

Explanation:

The correct answer is Option (2) → 403

Where:

  • $p_0$ = Price in base year ($1987$)
  • $p_1$ = Price in current year ($2015$)
  • $q_0$ = Quantity in base year ($1987$)

Sector

$q_0$​ (1987)

$p_0$​ (1987)

$p_1$​ (2015)

$p_1​q_0$​

$p_0​q_0$​

Commercial

5416

1.97

10.92

$59,142.72$

$10,669.52$

Residential

15,293

2.32

6.16

$94,204.88$

$35,479.76$

Industrial

21,287

0.79

5.13

$109,202.31$

$16,816.73$

Agriculture

9473

2.25

8.10

$76,731.30$

$21,314.25$

Total

 

   

$\sum p_1 q_0 = 339,281.21$

$\sum p_0 q_0 = 84,280.26$

 

$\text{(Laspeyres Index) } I_{2015} = \frac{10.92 \times 5416 + 6.16 \times 15293 + 5.13 \times 21287 + 8.10 \times 9473}{1.97 \times 5416 + 2.32 \times 15293 + 0.79 \times 21287 + 2.25 \times 9473} \times 100$

$= \frac{339281.21}{84280.26} \times 100$

$= 403$