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Question
The price of relatives and weights of a set of commodities are given below:
| Commodity | A | B | C | D |
| Price relatives | 125 | 120 | 127 | 119 |
| Weights | x | 2x | y | y + 3 |
If the sum of the weights is 40 and the weighted average of price relatives index number is 122, find the numerical values of x and y.
Solution
Given x + 2x + y + (y + 3) = 40
or 3x + 2y = 37 …(i)
and I = the index for the set = 122
We have I = weighted average of price - relatives
= `(125 xx x + 120 xx 2x + 127 xx y + 119 xx (y + 3))/(x + 2x + y + (y +3)`
or 122 = `(125x + 240x + 127y + 119y + 357)/(3x + 2y + 3)`
or 122 = `(365x + 246y + 357)/(40)` ...[ Using (i) ]
or 365x + 246y + 357 = 4880
or 365x + 246y = 4523 ...(ii)
Solving (i) and (ii), we have x = 7and y = 8.
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