Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Calculate price index number for 1990 taking 2010 as the base year from the following data by simple aggregative method:

Item

Rice

Wheat

Pulses

Millets

Oil

Price in year 1990 (in ₹)

60

40

100

60

90

Price in year 2010 (in ₹)

140

60

205

70

100

Options:

150.00

164.29

172.50

185.12

Correct Answer:

164.29

Explanation:

The correct answer is Option (2) → 164.29

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

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

Where:

  • $\sum p_0$ = Total price of all items in the base year (1990)
  • $\sum p_1$ = Total price of all items in the current year (2010)

Calculation Table

Item

Price in 1990 ($p_0$​)

Price in 2010 ($p_1$​)

Rice

60

140

Wheat

40

60

Pulses

100

205

Millets

60

70

Oil

90

100

Total

$\sum p_0 = 350$

$\sum p_1 = 575$

 

Apply the formula:

$P_{01} = \frac{575}{350} \times 100$

$P_{01} \approx 1.64285 \times 100$

$P_{01} = 164.29$