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CA Foundation · Quantitative Aptitude · Index Numbers

For a set of goods, Laspeyres' price index is 125 and Laspeyres' quantity index is 120 (both on the same base). Given that the total value in the base year is ₹50,000 and Σp1q0 and Σp0q1 are computed from these indices, which statement is correct?

Laspeyres price index gives Σp1q0 = 1.25 × 50,000 = ₹62,500, while Laspeyres quantity index gives Σp0q1 = 1.20 × 50,000 = ₹60,000. Each index uses base-year value as its denominator, so the first statement is correct.

  1. AΣp1q0 = ₹62,500 and Σp0q1 = ₹60,000Correct
  2. BΣp1q0 = ₹60,000 and Σp0q1 = ₹62,500
  3. CΣp1q0 = ₹62,500 and Σp0q1 = ₹62,500
  4. DΣp1q0 = ₹75,000 and Σp0q1 = ₹60,000

Explanation

Laspeyres price index = Σp1q0/Σp0q0 = 1.25, so Σp1q0 = 1.25 × 50,000 = 62,500. Laspeyres quantity index = Σp0q1/Σp0q0 = 1.20, so Σp0q1 = 60,000. Swapping them is the usual error of mixing the two indices.

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