Question

Tick (✓) the correct answer:
A man sold two chairs for Rs 500 each. On one he gains 20% and on the other he loses 12%. His net gain or loss per cent is
(a) 1.5% gain
(b) 2% gain
(c) 1.5% loss
(d) 2% loss

Answer 1

(a) 1.5% gain

​ $$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{chair}=\mathrm{Rs}500 \\ \mathrm{Gain}\mathrm{percentage}=20\% \\ \therefore \mathrm{CP}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{chair}=\left\{\frac{100}{\left(100+\mathrm{gain}\%\right)}\times \mathrm{SP}\right\} \end{gathered}$$
$$\begin{gathered} =\mathrm{Rs}.\left\{\frac{100}{\left(100+20\right)}\times 500\right\} \\ =\mathrm{Rs}.\left(\frac{100}{120}\times 500\right) \\ =\mathrm{Rs}.416.67 \end{gathered}$$

$$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{chair}=\mathrm{Rs}.500 \\ \mathrm{Loss}\mathrm{percentage}=12\% \\ \therefore \mathrm{CP}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{chair}=\left\{\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right\} \end{gathered}$$
$$\begin{gathered} =\mathrm{Rs}.\left\{\frac{100}{\left(100-12\right)}\times 500\right\} \\ =\mathrm{Rs}.\left(\frac{100}{88}\times 500\right) \\ =\mathrm{Rs}.568.18 \end{gathered}$$

$\mathrm{Total}\mathrm{CP}\mathrm{of}\mathrm{the}\mathrm{two}\mathrm{chairs}=\mathrm{Rs}.\left(416.67+568.18\right)$
$=Rs.984.85$
$TotalSPofthetwochairs=Rs.\left(500\times 2\right)$
$=Rs.1000$
$$\begin{gathered} SinceSP>CP,thereisagaininthewholetransaction. \\ Now,gain=Rs.\left(1000-984.85\right) \\ =Rs.15.15 \\ \therefore Gainpercentage=\left(\frac{gain}{CP}\times 100\right)\% \\ =\left(\frac{15.15}{984.85}\times 100\right)\% \\ =1.5\% \end{gathered}$$