Question

A dealer sold a camera for Rs 1080 gaining $\frac{1}{8}$ of its cost price. Find (i) the cost price of the camera, and (ii) the gain per cent earned by the dealer.

Answer 1

$$\begin{gathered} \mathrm{SP}\mathrm{of}\mathrm{the}\mathrm{camera}=\mathrm{Rs}.1080 \\ \mathrm{Let}\mathrm{Rs}x\mathrm{be}\mathrm{the}\mathrm{CP}. \\ \mathrm{Gain}=\mathrm{Rs}.\frac{1}{8}x...\left(\mathrm{i}\right) \\ \mathrm{Also},\mathrm{gain}=\mathrm{SP}-\mathrm{CP} \\ =\mathrm{Rs}.(1080-x)...\left(\mathrm{ii}\right) \\ \mathrm{From}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right),\mathrm{we}\mathrm{have}: \\ \frac{1}{8}x=1080-x \\ \Rightarrow x=8640-8x \\ \Rightarrow 9x=8640 \\ \Rightarrow \mathrm{x}=960 \\ \therefore \mathrm{CP}=\mathrm{Rs}.960 \\ \mathrm{Now},\mathrm{gain}=\frac{1}{8}\mathrm{x} \\ =\frac{960}{8} \\ =\mathrm{Rs}.120 \\ \therefore \mathrm{Gain}\mathrm{percentage}=(\frac{120}{960}\times 100)\% \\ =12\frac{1}{2}\% \end{gathered}$$