Question

By selling an umbrella for ₹ 336, a shopkeeper loses 4%. At what price must he sell it to gain 4%?

Answer 1

Let the CP of the umbrella be ₹x.
SP of the umbrella = ₹336
Loss = 4% of ₹x = $₹\frac{4}{100}x$
CP − Loss = SP
$$\begin{gathered} \Rightarrow x-\frac{4}{100}x=336 \\ \Rightarrow \frac{96}{100}x=336 \\ \Rightarrow x=₹350 \end{gathered}$$
∴ CP of the umbrella = ₹350
Now, for gain of 4%,
SP = CP + Gain
$$\begin{gathered} \Rightarrow \mathrm{SP}=350+\frac{4}{100}\times 350 \\ \Rightarrow \mathrm{SP}=350+14 \\ \Rightarrow \mathrm{SP}=₹364 \end{gathered}$$
Hence, in order to gain 4%, the umbrella should be sold for ₹364.