CA Foundation · Quantitative Aptitude · Index Numbers
In constructing a cost of living index by the weighted average of price relatives method, three items have price relatives 120, 150 and 110 with weights 4, 2 and 4 respectively. What is the index number?
The index is 122. Multiply each price relative by its weight, giving 480, 300 and 440, which total 1220, then divide by the total weight of 10. A simple average of the relatives, 126.7, ignores the weights and is incorrect.
- A122Correct
- B126.7
- C120
- D128
Explanation
Index = ΣIW/ΣW, where I is the price relative. ΣIW = 120×4 + 150×2 + 110×4 = 480+300+440 = 1220 and ΣW = 10, so the index is 122. The simple average of relatives, 126.7, ignores the weights and is therefore wrong.
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