Question

The $C.P$ of two watches taken together is $Rs840$. If by selling one at a profit of $16\%$ and the other at a loss of $12\%$, there is no gain or loss in the whole transaction then find the $C.P$. of each watch.

Answer 1

Let the $C.P$ of $1^{st}$ watch bs $Rsx$.

Then $C.P$ of $2^{nd}$ watch be $Rs840-x$

$S.P$ of $1^{st}$ watch $=\frac{116x}{100}\left(16\%profit\right)$

$S.P$ of $2^{nd}$ watch $=\frac{88(840-x)}{100}\left(12\%loss\right)$

No loss / gain.

$\Rightarrow 840=\frac{116x}{100}+\frac{88(840-x)}{100}$

$\Rightarrow 840\times 100=116x-88x+840\times 88$

$\Rightarrow 84000=28x+73920$

$\Rightarrow 28x=84000-73920$

$=x=\frac{10080}{28}=360$

$C.P$ of $1^{st}$ watch $=Rs360$

$C.P$ of $2^{nd}$ watch $=Rs(840-x)$

$=Rs(840-360)$

$=Rs480$