Raghavan purchase a scooter at $$\frac{13}{15}$$ of its selling price and sold it at 12% more than its selling price. His gain is -

$$\eqalign{ & {\text{Let S}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Then,}} \cr & {\text{C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\frac{{13}}{{15}}x, \cr & {\text{Receipt}} = 112\% {\text{ of Rs}}{\text{. }}x \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{28}}{{25}}x \cr & {\text{Gain}} = {\text{Rs}}.\left( {\frac{{28x}}{{25}} - \frac{{13x}}{{15}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\frac{{19x}}{{75}} \cr & \therefore {\text{Gain}}\% \cr & = \left( {\frac{{19x}}{{75}} \times \frac{{15}}{{13x}} \times 100} \right)\% \cr & = \frac{{380}}{{13}}\% \cr & = 29\frac{3}{{13}}\% \cr} $$