Question

By selling an umbrella for R 115.20, Kishan loses 10%. At what price must he sell it to gain 5%?

Answer 1

SP of the umbrella = Rs 115.20
Loss = 10%
$$\begin{gathered} \mathrm{CP}\mathrm{o}\mathrm{f}\mathrm{the}\mathrm{umbrella}=\frac{100}{100-\mathrm{loss}}\times \mathrm{SP} \\ =\mathrm{Rs}\frac{100}{100-10}\times 115.20 \\ =\mathrm{Rs}\frac{100}{90}\times 115.20 \\ =\mathrm{Rs}128 \end{gathered}$$

Now, CP = Rs 128 and desired gain = 5%

$$\begin{gathered} \therefore \mathrm{Desired}\mathrm{S}\mathrm{P}=\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs}\frac{105}{100}\times 128 \\ =\mathrm{Rs}134.4 \end{gathered}$$

Hence, the desired selling price is Rs 134.4