Question

Mark (✓) against the correct answer:
On selling a chair for Rs 680, a man loses 15%. To gain 15%, it must be sold for
(a) Rs 800
(b) Rs 860
(c) Rs 920
(d) Rs 884

Answer 1

(c) Rs.920

$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}680 \\ \mathrm{Loss}\mathrm{percentage}=15\% \\ \mathrm{Now},\mathrm{CP}=\left\{\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right\} \end{gathered}$$
$$\begin{gathered} =\mathrm{Rs}.\left\{\frac{100}{\left(100-15\right)}\times 680\right\} \\ =\mathrm{Rs}.\left(\frac{100}{85}\times 680\right) \\ =\mathrm{Rs}.800 \end{gathered}$$
$\therefore \mathrm{Desired}\mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{CP}\right\}$
$$\begin{gathered} =\mathrm{Rs}\left\{\frac{\left(100+15\right)}{100}\times 800\right\} \\ =\mathrm{Rs}\left(\frac{115}{100}\times 800\right) \\ =\mathrm{Rs}920 \end{gathered}$$