The price relatives and weights of a set of commodities are given as :
| Commodity | P | Q | R |
| Price Relative | 100 | 130 | 180 |
| Weight | x | 2x | y |
If the sum of weights is 54 and index for the set is 130, then the values of x and y are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $x=15, y = 9$
Sum of weights:
$x+2x+y=54$
$3x+y=54$ ...(1)
Weighted average index is,
$I=\frac{∑(P_R×W)}{∑W}$
$⇒130=\frac{100x+130(2x)+180y}{54}$
$⇒360x+180y=7020$ ...(2)
From (1) and (2),
$360x+180(54-3x)=7020$
$-180x+9720=7020$
$-180x=-2700$
$x=15$
and,
$y=54-3(15)$
$y=54-45=9$