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

The cost of living index for a class of workers rose from 120 to 150 between two years. A worker's wage was ₹24,000 in the earlier year. To keep the same real wage, what wage must the worker receive in the later year, and what is the extra compensation needed?

The worker needs ₹30,000, an extra ₹6,000. The index rose from 120 to 150, an increase of 25 percent, so the earlier wage of ₹24,000 must be multiplied by 150/120 to keep real purchasing power unchanged.

  1. A₹30,000 wage; ₹6,000 extraCorrect
  2. B₹30,000 wage; ₹4,800 extra
  3. C₹19,200 wage; ₹4,800 less
  4. D₹36,000 wage; ₹12,000 extra

Explanation

Required wage = 24,000 × 150/120 = ₹30,000. Extra = 30,000 − 24,000 = ₹6,000. Option ₹4,800 uses 20% rise instead of the true 25%. Option ₹19,200 inverts the ratio. Option ₹36,000 adds 50%.

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