Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Calculate the price index number for the following data using weighted aggregative method:

Commodity

Unit

Weight

Price

Base year

Current year

P

Quintal

14

90

120

Q

Kg

20

10

17

R

Dozen

35

40

60

S

Litre

15

50

93

Options:

145.20

152.77

170.10

161.45

Correct Answer:

152.77

Explanation:

The correct answer is Option (2) → 152.77

The Weighted Aggregative Price Index ($P_{01}$) is given by:

$P_{01} = \frac{\sum p_1 W}{\sum p_0 W} \times 100$

Calculation Table:

Commodity

Weight (W)

$p_0$​ (Base)

$p_1$​ (Current)

$p_1​W$

$p_0​W$

P

14

90

120

$120 \times 14 = 1680$

$90 \times 14 = 1260$

Q

20

10

17

$17 \times 20 = 340$

$10 \times 20 = 200$

R

35

40

60

$60 \times 35 = 2100$

$40 \times 35 = 1400$

S

15

50

93

$93 \times 15 = 1395$

$50 \times 15 = 750$

Total

 

 

 

$\sum p_1 W = 5515$

$\sum p_0 W = 3610$

 

Apply the formula:

$P_{01} = \frac{5515}{3610} \times 100$

$P_{01} \approx 1.5277 \times 100$

$P_{01} = 152.77$