Question:
By selling an umbrella for ₹ 336, a shopkeeper loses 4%. At what price must he sell it to gain 4%?
Solution:
Let the CP of the umbrella be ₹ $x$.
SP of the umbrella = ₹336
Loss $=4 \%$ of $₹ x=₹ \frac{4}{100} x$
CP $-$ Loss $=$ SP
$\Rightarrow x-\frac{4}{100} x=336$
$\Rightarrow \frac{96}{100} x=336$
$\Rightarrow x=₹ 350$
$\therefore$ CP of the umbrella $=₹ 350$
Now, for gain of $4 \%$,
SP $=\mathrm{CP}+$ Gain
$\Rightarrow \mathrm{SP}=350+\frac{4}{100} \times 350$
$\Rightarrow \mathrm{SP}=350+14$
$\Rightarrow \mathrm{SP}=₹ 364$
Hence, in order to gain $4 \%$, the umbrella should be sold for ₹ 364 .