Question

The price of six different commodities for year $2009$ and year $2011$ are as follows:

Commodities	$A$	$B$	$C$	$D$	$E$	$F$
Price in $2009\left(Rs\right)$	$35$	$80$	$25$	$30$	$80$	$x$
Price in $2011\left(Rs\right)$	$50$	$y$	$45$	$70$	$120$	$105$

The Index number for the year $2011$ taking $2009$ as the base year for the above data was calculated to be $124$. Find the values of $x$ and $y$ if the total price in $2009$ is $Rs.360$

Answer 1

Commodities	Prices in $2009$	Prices in $2011$
$A$	$35$	$50$
$B$	$80$	$y$
$C$	$25$	$45$
$D$	$30$	$70$
$E$	$80$	$120$
$F$	$x$	$105$
	$\sum P_0=250+x$	$\sum P_1=390+y$

Given, $\sum P_0=360$
$x+250=360$
$x=110$

$\frac{\sum P_1}{\sum P_0}\times 100=P_{01}$

$\frac{390+y}{360}\times 100=125$

$390+y=\frac{125\times 360}{100}$

$390+y=450$

$y=60$

Hence, the value of $x$ is $Rs.110$ and $y$ is $Rs.60$.