Question

On selling an article for Rs 48, a shopkeeper loses 20%. In order to gain 20%, what would be the selling price?
(a) Rs 52
(b) Rs 56
(c) Rs 68
(d) Rs 72

Answer 1

$$\begin{gathered} \left(\mathrm{d}\right)\mathrm{Rs}72 \\ \mathrm{SP}=\mathrm{Rs}48 \\ \mathrm{Loss}=20\% \\ \mathrm{Now},\mathrm{CP}=\frac{100}{100-\mathrm{loss}\%}\times \mathrm{SP} \\ =\mathrm{Rs}\left(\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right) \\ =\mathrm{Rs}\left(\frac{100}{\left(100-20\right)}\times 48\right) \\ =\mathrm{Rs}\left(\frac{100}{80}\times 48\right) \\ =\mathrm{Rs}60 \end{gathered}$$

$\therefore \mathrm{Desired}\mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{CP}\right\}$

$$\begin{gathered} =\left\{\frac{\left(100+20\right)}{100}\times 60\right\} \\ =\mathrm{Rs}\left(\frac{12}{10}\times 60\right) \\ =\mathrm{Rs}72 \end{gathered}$$