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

If the sum of weights is 54 and index for the set is 130, then the values of x and y are

x=15, y = 9

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,

$y=54-3(15)$

$y=54-45=9$