Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Index Numbers and Time Based Data

Question:

Based on the data on the expenses of middle-class families in a certain city, calculate the cost-of-living index during the year 2003 as compared with 1990:

Expenses

Year

Food

Fuel

Clothing

Rent

Miscellaneous

Price (in ₹)

2003

1500

250

750

300

425

Price (in ₹)

1990

1400

200

400

200

250

Options:

121.45

142.10

131.63

155.25

Correct Answer:

131.63

Explanation:

The correct answer is Option (3) → 131.63

The Cost-of-Living Index ($I$) is calculated as:

$I = \frac{\sum P_1}{\sum P_0} \times 100$

Where:

  • $\sum P_1$ = Total expenses in the current year (2003)
  • $\sum P_0$ = Total expenses in the base year (1990)

Calculation Table

Expense Category

Price in 1990 ($P_0$​)

Price in 2003 ($P_1$​)

Food

1400

1500

Fuel

200

250

Clothing

400

750

Rent

200

300

Miscellaneous

250

425

Total

$\sum P_0 = 2450$

$\sum P_1 = 3225$

 

Apply the formula:

$I = \frac{3225}{2450} \times 100$

$I \approx 1.31632 \times 100$

$I = 131.63$