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.

Answer 1

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.