Question

The index number by the method of aggregates for the year $2010$, taking $2000$ as the base year, was found to be $116$. If sum of the prices in the year $2000$ is Rs. $300$, find the values of $x$ and $y$ in the data given below:

Commodity	$A$	$B$	$C$	$D$	$E$	$F$
Price in the year $2000$(rs.)	$50$	$x$	$30$	$70$	$116$	$20$
Price in the year $2010$(rs.)	$60$	$24$	$y$	$80$	$120$	$28$

Answer 1

First we tabulate the given data in the following form:

Commodities	Price in $2000$ (in Rs.) $P_0$	Price in $2010$ (in Rs.) $P_1$
$A$	$50$	$60$
$B$	$x$	$24$
$C$	$30$	$y$
$D$	$70$	$80$
$E$	$116$	$120$
$F$	$20$	$28$
	$\sum P_0=286+x$	$\sum P_1=312+y$

Given: $\sum P_0=300$ $\Rightarrow$ $286+x=300\Rightarrow$ $x=14$
Index number$=116$
$\therefore$ Using $P_{01}=\frac{\sum P_1}{\sum P_0}\times 100$
$116\times \frac{312+y}{300}\times 100$
$y=36$
$\therefore$ $x=14$ and $y=36$