The price relatives and weights of a set of commodities are given as :
| Commodity | A | B | C |
| Price Relative | 150 | 130 | 180 |
| Weight | x | 3y | y |
If the sum of weights is 30 and the index for the set is 144, then the values of x and y are :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $x=6, y = 6$
Weighted Price Index, $I=\frac{∑(P_r×W)}{∑W}$
$⇒144=\frac{(150x+130(3y)+180y)}{30}$
$⇒150x+570y=4320$ ....(1)
and,
$x+4y=30$ ....(2)
from (1) and (2)
$150(30-4y)+570y=4320$
$180=30y$
$y=6$ and $x=6$