The price relatives and weights of a set of commodities are given as :

If the sum of weights is 30 and the index for the set is 144, then the values of x and y are :

$x=6, y = 6$

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 $x=6$