Question

Three articles are sold for $Rs.1,890,Rs.2,400$ and $Rs.1,135$ respectively. The first article is sold at $12.5\%$ profit and the second at $20\%$ profit. If on the whole a loss of $3\frac{1}{8}\%$ is made, find the cost price of the third article.

Answer 1

Given, for the first article
$S.P=Rs1,890$
Profit $=12.5$ %
Now, with this S.P. and for Profit % $=\frac{S.P.-C.P.}{C.P.}\times 100=12.5$ %
$=>\frac{1,890-C.P.}{C.P.}\times 100=12.5$
$=>1,890-C.P.=0.125C.P.$
$1.125C.P.=1,890$
$=>C.P.=Rs1,680$

And for another TV,
$S.P=Rs2,400$
Profit $=20$ %

So, Profit % $=\frac{S.P.-C.P.}{C.P.}\times 100=20$
$=>\frac{2,400-C.P.}{C.P}\times 100=20$
$=>2,400-C.P.=0.20C.P.$
$=>1.2C.P=2,400$
$=>C.P.=Rs2,000$


Now Total S.P. $=Rs1,890+Rs2,400+Rs1,135=Rs5,425$

And Total Loss % $=\frac{TotalC.P.-TotalS.P.}{TotalC.P.}\times 100=\frac{25}{8}$ %
$=>\frac{TotalC.P.-5,425}{TotalC.P.}\times 100=\frac{25}{8}$
on solving we get
Total C.P $=Rs5,600$


Hence, C.P. of third article = $Rs5,600-Rs1,680-Rs2,000=Rs1,920$