Question

Hema bought two pairs of jeans for Rs 725 each. She sold one of them at a gain of 8% and the other at a loss of 4%. Find her gain or loss per cent in the whole transaction.

Answer 1

CP of one jeans = Rs 725
Gain percentage = 8%

$$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{one}jeans=\mathrm{Rs}\left\{\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP}\right\} \\ =\mathrm{Rs}\left\{\frac{100+8}{100}\times 725\right\} \\ =\mathrm{Rs}\left\{\frac{108}{100}\times 725\right\} \\ =\mathrm{Rs}783 \end{gathered}$$

CP of the other jeans = Rs 725
Loss percentage = 4%

$$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{the}\mathrm{other}\mathrm{j}\mathrm{eans}=\left\{\frac{100-\mathrm{loss}\%}{100}\times \mathrm{CP}\right\} \\ =\left\{\frac{100-4}{100}\times 725\right\} \\ =\left\{\frac{96}{100}\times 725\right\} \\ =\mathrm{Rs}696 \end{gathered}$$

Total CP of the two pairs of jeans = Rs ($725\times 2$) = Rs 1450
Total SP of the two pairs of jeans = Rs (696 + 783) = Rs1479
Since SP >CP, there is a gain in the whole transaction.

Now, gain = Rs (1479 − 1450) = Rs 29
$$\begin{gathered} \therefore \mathrm{Gain}\mathrm{percentage}=\left\{\frac{\mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}}{\mathrm{to}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{C}\mathrm{P}}\times 100\right\}\% \\ =\left\{\frac{29}{1450}\times 100\right\}\% \\ =2\% \end{gathered}$$
Hence, Hema gains 2% on the whole transaction.