Using simple average of relatives method, the price index for 2011, taking 2001 as base year, was found to be 127. If $∑p_0= 263,$ then x and y from the following data are :

$x=50, y = 27 $

The correct answer is Option (1) → $x=50, y = 27$

Price index = $\frac{1}{n}∑\left(\frac{P_1}{P_0}×100\right)$

The price index for 2011 is given as 127,

$127=\frac{1}{6}∑\left(\frac{P_1}{P_0}×100\right)$

$762=∑\left(\frac{P_1}{P_0}×100\right)$

$⇒125+125+\frac{6100}{x}+110+\frac{100y}{18}+130=762$

$490+\frac{6100}{x}+\frac{100y}{18}=762$

$\frac{6100}{x}+\frac{100y×18}{18}=4896$

$\frac{6100}{x}+100y=4896$

$(x=50\,and\,y=27)$ satisfies.