Question

Vinod sold a watch to Alex at a gain of 12% and Alex had to sell it to Shweta at a loss of 5%. If Shweta paid Rs 1330 for it, how much did Vinod pay for the watch?

Answer 1

SP of the watch for Alex= Rs 1330
Loss percentage for Alex = 5%

$$\begin{gathered} \mathrm{CP}\mathrm{for}\mathrm{A}\mathrm{lex}=\frac{\mathrm{SP}\times 100}{100-\mathrm{loss}\%} \\ =\frac{1330\times 100}{100-5} \\ =\frac{133000}{95} \\ =\mathrm{Rs}1400 \end{gathered}$$

Now, SP for Vinod = CP for Alex = Rs 1400
Gain percentage of the watch for Vinod = 12%
$$\begin{gathered} \mathrm{CP}\mathrm{of}\mathrm{the}\mathrm{watch}\mathrm{for}\mathrm{Vinod}=\frac{\mathrm{SP}\times 100}{100+\mathrm{gain}\%} \\ =\mathrm{Rs}\frac{1400\times 100}{100+12} \\ =\mathrm{Rs}\frac{140000}{112}=\mathrm{Rs}1250 \end{gathered}$$

Thus, Vinod paid Rs 1250 for the watch.