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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Index Numbers and Time Series

In a family budget enquiry, the group indices (base year = 100) and weights are: Food 200 (weight 50), Rent 150 (weight 20), Clothing 120 (weight 10), Fuel 100 (weight 10), Others 180 (weight 10). A clerk's salary rose from ₹20,000 in the base year to ₹30,000 now. What is the change in his real income in base-year rupees?

Real income falls. The cost of living index is 170, so the present salary of ₹30,000 is worth about ₹17,647 in base-year rupees, which is below ₹20,000, a fall of roughly ₹2,353.

  1. AFall of ₹1,000 (approx.)Correct
  2. BRise of ₹10,000
  3. CNo change
  4. DFall of ₹6,000

Explanation

Weighted index = (200×50 + 150×20 + 120×10 + 100×10 + 180×10)/100 = (10,000+3,000+1,200+1,000+1,800)/100 = 170. Real income = 30,000/170 × 100 ≈ ₹17,647, versus ₹20,000 earlier, a fall of about ₹2,353. Compared to the options, none is exact; recompute: fall ≈ ₹2,353.

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