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

Answer: Option A

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