Find the rate percent if the banker’s gain on a certain sum due two and a half year hence is $$\frac{1}{5}$$ of the banker’s discount.

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{Banker's}}\,{\text{Discount}} \cr & = {\text{Rs}}{\text{.}}\,10 \cr & {\text{Then,}}\,{\text{Banker's}}\,{\text{Gain}} \cr & = {\text{Rs}}{\text{.}}\,\frac{1}{5} \times 10 \cr & = {\text{Rs}}{\text{.}}\,2 \cr & T.D. = \left( {B.D. - B.G.} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {10 - 2} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,8 \cr & {\text{Sum}} = \frac{{10 \times 8}}{{10 - 8}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{80}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,40 \cr} $$
S.I. on Rs. 40 for 2.5 year is Rs. 10
$$\eqalign{ & {\text{Therefore,}} \cr & {\text{Rate}} = \frac{{100 \times 10}}{{40 \times 2.5}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$