Question 17 of 19intermediate🔧 ApplyNumerical5 marks

An enquiry into the budgets of the middle class families in a certain city gave the following information;

Expenses on itemsFood 35%Fuel 10%Clothing 20%Rent 15%Misc. 20%
Price (in Rs) in 20041500250750300400
Price (in Rs) in 19951400200500200250

What is the cost of living index during the year 2004 as compared with 1995?

Correct Answer

The cost of living index for the year 2004 as compared with 1995 is 134.50. This indicates that the cost of living has increased by 34.50% from 1995 to 2004.

Exercise: EXERCISES | Q: 19 | (Page Page 14)
For More Understanding

Explanation

This question requires calculating the Consumer Price Index (CPI) using the weighted aggregative method. The formula CPI = ΣWR/ΣW is demonstrated in Example 4 of the textbook context. Students need to calculate the price relative (R) for each item by dividing current year price by base year price and multiplying by 100, then multiply by respective weights, sum them up, and divide by total weight.

Solution Steps

  1. Step 1: Calculate Price Relative (R) for each item using formula R = (P₁/P₀) × 100

  2. Food: R = (1500/1400) × 100 = 107.14

  3. Fuel: R = (250/200) × 100 = 125

  4. Clothing: R = (750/500) × 100 = 150

  5. Rent: R = (300/200) × 100 = 150

  6. Misc: R = (400/250) × 100 = 160

  8. Step 2: Calculate WR (Weight × Price Relative) for each item

  9. Food: WR = 35×107.1435 \times 107.14 = 3750

  10. Fuel: WR = 10×12510 \times 125 = 1250

  11. Clothing: WR = 20×15020 \times 150 = 3000

  12. Rent: WR = 15×15015 \times 150 = 2250

  13. Misc: WR = 20×16020 \times 160 = 3200

  15. Step 3: Sum all WR values

  16. ΣWR = 3750 + 1250 + 3000 + 2250 + 3200 = 13450

  18. Step 4: Apply CPI formula

  19. CPI = ΣWR/ΣW = 13450/100 = 134.50

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