Question

Wasim bought two cricket bats for Rs 560 and Rs 240 respectively. He sells the first bat at a gain of 15% and the second one at a loss of 5%. Find his gain or loss per cent in the whole transaction.

Answer 1

CP of the first bat = Rs 560
Gain percentage = 15%

$$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{the}\mathrm{first}\mathrm{bat}=\mathrm{Rs}\left\{\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP}\right\} \\ =\mathrm{Rs}\left\{\frac{100+15}{100}\times 560\right\} \\ =\mathrm{Rs}\left\{\frac{115}{100}\times 560\right\} \\ =\mathrm{Rs}644 \end{gathered}$$

CP of the second bat = Rs 240
Loss percentage = 5%

$$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{the}\mathrm{second}\mathrm{b}\mathrm{at}=\mathrm{Rs}\left\{\frac{100-\mathrm{loss}\%}{100}\times \mathrm{CP}\right\} \\ =\mathrm{Rs}\left\{\frac{100-5}{100}\times 240\right\} \\ =\mathrm{Rs}\left\{\frac{95}{100}\times 240\right\} \\ =\mathrm{Rs}228 \end{gathered}$$

Total CP of the two bats = Rs (560 + 240) = Rs 800
Total SP of the two bats = Rs (644 + 228) = Rs 872

Since SP >CP, there is gain in the whole transaction.
Now, gain = Rs (872 − 800) = Rs 72
=$$\begin{gathered} \therefore \mathrm{Gain}\mathrm{percentage}=\left\{\frac{\mathrm{gain}}{\mathrm{total}\mathrm{CP}}\times 100\right\}\% \\ =\left\{\frac{72}{800}\times 100\right\}\% \\ =9\% \end{gathered}$$

Wasim gains 9% on the whole transaction.