CA Foundation · Quantitative Aptitude · Index Numbers
The time reversal test for an index number formula requires that, when the base year and current year are interchanged, the two resulting price indices (each expressed as a ratio, not a percentage) should have which relationship?
The product of the price index with year 0 as base and the index with year 1 as base must equal 1 (P01 × P10 = 1) under the time reversal test. Swapping the periods should give the reciprocal index, so the product of the two is unity.
- ATheir sum equals 1
- BTheir product equals 1Correct
- CTheir difference equals 1
- DTheir ratio equals 100
Explanation
The time reversal test requires P01 × P10 = 1, where P01 is the index with base 0 and P10 the index with base 1. Sum or difference equal to 1 is not the condition. Fisher's formula satisfies this because the square roots cancel in the product.
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