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

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Cost price}} = \frac{{13}}{{15}}{\text{ Selling price}} \cr & \frac{{{\text{Cost price}}}}{{{\text{Selling price}}}} = \frac{{13}}{{15}} \cr} $$
If they sold 12% more then its, old selling price.
So, new selling price is
$$\eqalign{ & = 15 + \frac{{12}}{{100}} \times 15 \cr & = 16.8 \cr} $$
∴ Profit = Selling price - Cost price
              = 16.8 - 13
              = 3.8
$$\eqalign{ & {\text{Profit }}\% = \frac{{3.8}}{{13}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 29\frac{3}{{13}}\% \cr} $$