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CA Foundation · Quantitative Aptitude · Index Numbers

A price index with base 2016 = 100 equals 160 in 2024. A statistician claims that the index shows the cost of living rose by 60% for every household. Another statistician says the cost of a household's basket rose by 60% only if its spending pattern matched the index weights. For a household whose spending is entirely on a commodity whose price rose from ₹50 to ₹70, what is the rise in its cost of living, and does it equal the index rise?

The household's cost of living rises by 40%, which differs from the index rise of 60%. Its spending is wholly on one commodity going from ₹50 to ₹70, a 40% rise. The general index reflects average weights, so it misrepresents any household with a different spending pattern.

  1. A40%, which differs from the index rise of 60%Correct
  2. B20%, which differs from the index rise of 60%
  3. C60%, which equals the index rise
  4. D40%, which equals the index rise

Explanation

The household buys only one commodity, so its cost of living rises by (70−50)/50 × 100 = 40%. The index shows 60%, so the figures differ because the household's weights differ from the index weights. The 20% option uses the price difference instead of the percentage change.

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