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 :
| Commodities | A | B | C | D | E | F |
| Prices (in ₹ ) in 2001 | 80 | 70 | x | 20 | 18 | 25 |
| Prices (in ₹ ) in 2011 | 100 | 87.50 | 61 | 22 | y | 32.50 |
Answer & explanation
Correct answer: option 1
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.