Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Calculate index numbers from the following data by simple aggregate method taking prices of 1995 as base period.

Commodity

  Year  

  A  

  B  

  C  

  D  

Price (in Rupees/unit)

1995

80

50

90

30

2005

95

60

100

45

Options:

160

150

130

120

Correct Answer:

120

Explanation:

The correct answer is Option (4) → 120

To calculate the price index number using the simple aggregate method, we use the following formula:

$P_{01}​=\frac{∑P_1}{​∑P_0}​​×100$

Where:

  • $∑P_0$​ is the sum of prices in the base year (1995).
  • $∑P_1$​ is the sum of prices in the current year (2005).

Calculation of Sums

Commodity

Price in 1995 ($P_0$​)

Price in 2005 ($P_1$​)

A

80

95

B

50

60

C

90

100

D

30

45

Total

$∑P_0​=250$

$∑P_1​=300$

Calculation of Index Number

Substituting the values into the formula:

$P_{01}​=\frac{250}{300}​×100$

$P_{01}​=1.2×100$

$P_{01}​=120$

The price index number for the year 2005, taking 1995 as the base year, is 120. This indicates a 20% increase in the aggregate price level from 1995 to 2005.