Question

Parvinder sold a watch at a loss of 5 per cent. If he had sold that watch for Rs 27 more, he would have gained 7 per cent. Find the cost price of the watch.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{CP}\mathrm{of}\mathrm{the}\mathrm{watch}=\mathrm{Rs}x \\ \mathrm{Loss}\%=5\% \\ \Rightarrow \mathrm{loss}\%=\left[\frac{\mathrm{loss}}{\mathrm{CP}}\times 100\right]\% \\ \Rightarrow 5=\left(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100\right) \\ \Rightarrow 20\mathrm{loss}=\mathrm{CP} \\ \Rightarrow 20\left(\mathrm{CP}-\mathrm{SP}\right)=\mathrm{CP} \\ \Rightarrow 20\mathrm{CP}-20\mathrm{SP}=\mathrm{CP} \\ \Rightarrow 20\mathrm{SP}=19\mathrm{CP} \\ \Rightarrow \mathrm{SP}=\mathrm{Rs}\left(\frac{19}{20}\mathrm{CP}\right)=\mathrm{Rs}\left(\frac{19x}{20}\right).......\left(1\right) \\ \mathrm{gain}\%=7\% \\ \Rightarrow \mathrm{gain}\%=\left[\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right]\% \\ \Rightarrow 7=\left[\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right] \\ \Rightarrow 100\mathrm{gain}=7\mathrm{CP} \\ \Rightarrow 100\left(\mathrm{SP}-\mathrm{CP}\right)=7\mathrm{CP} \\ \Rightarrow 100\mathrm{SP}-100\mathrm{CP}=7\mathrm{CP} \\ \Rightarrow 100\mathrm{SP}=107\mathrm{CP} \\ \Rightarrow \mathrm{SP}=\frac{107}{100}\mathrm{CP} \\ \Rightarrow \mathrm{SP}=\mathrm{Rs}\left(\frac{107x}{100}\right).......\left(2\right) \\ \mathrm{According}\mathrm{to}\mathrm{question}, \\ \left(\frac{107x}{100}\right)-\left(\frac{19x}{20}\right)=27 \\ \Rightarrow \frac{107x-95x}{100}=27 \\ \Rightarrow \frac{12x}{100}=27 \\ \Rightarrow x=\frac{2700}{12}=225 \\ \mathrm{So},\mathrm{CP}=\mathrm{Rs}225 \end{gathered}$$