CA Foundation · Quantitative Aptitude · Index Numbers
In a family budget inquiry, the groups Food, Housing and Miscellaneous carry weights 50, 30 and 20, with price relatives 160, x and 100 respectively. If the cost of living index by the weighted relatives method is 133, what is the value of x?
The price relative for Housing is 110. With weights totalling 100, the weighted sum of relatives must be 13,300. Food contributes 8,000 and Miscellaneous 2,000, leaving 3,300 for Housing. Dividing by its weight of 30 gives x = 110.
- A100
- B110Correct
- C120
- D130
Explanation
ΣW = 100, so ΣWI = 133 × 100 = 13,300. Then 50×160 + 30x + 20×100 = 8,000 + 30x + 2,000 = 13,300, giving 30x = 3,300 and x = 110. Check: (8,000 + 3,300 + 2,000)/100 = 133.
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