Question

A shopkeeper sold two fans for Rs 990 each. On one he gains 10% and on the other he loses 10%. Calculate his gain or loss per cent in the whole transaction.

Answer 1

SP of one fan = Rs 990
Gain percentage = 10%
$$\begin{gathered} \mathrm{CP}\mathrm{of}\mathrm{one}\mathrm{f}\mathrm{an}=\left\{\frac{100}{100+\mathrm{gain}\%}\times \mathrm{SP}\right\} \\ =\left\{\frac{100}{100+10}\times 990\right\} \\ =\left\{\frac{100}{110}\times 990\right\} \\ =\mathrm{Rs}.900 \end{gathered}$$

SP of the other fan =Rs 900
Loss percentage = 10%
$$\begin{gathered} \mathrm{Its}\mathrm{CP}=\left\{\frac{100}{100-\mathrm{loss}\%}\times \mathrm{SP}\right\} \\ =\left\{\frac{100}{100-10}\times 990\right\} \\ =\left\{\frac{100}{90}\times 990\right\} \\ =\mathrm{Rs}1100 \end{gathered}$$

Total CP of the two fans = Rs (900 + 1100) = Rs 2000
Total SP of the two fans = Rs (990 + 990) = Rs 1980
Since CP >SP, there is a loss in the whole transaction.
Now, loss = Rs (2000 − 1980) = Rs 20
$$\begin{gathered} \therefore Losspercentage=\left\{\frac{loss}{totalCP}\times 100\right\}\% \\ =\left\{\frac{20}{2000}\times 100\right\}\% \\ =1\% \end{gathered}$$
Hence, the shopkeeper incurs a loss of 1% in the whole transaction.