The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain

Answer: Option A

$$\begin{array}{rl}& \text{Sum}=\frac{B.D.\times T.D.}{B.D.-T.D.}\\ & =\frac{B.D.\times T.D.}{B.G.}\\ & \frac{T.D.}{B.G.}=\frac{\text{Sum}}{B.D.}\\ & =\frac{1650}{165}\\ & =10\end{array}$$
Thus, if B.G. is Rs. 1, T.D. = Rs. 10
If B.D. is Rs. 11, T.D. = Rs. 10
If B.D. is Rs. 165,
$$\begin{array}{rl}& T.D.=\text{Rs}\text{.}\frac{10}{11}\times 165\\ & =\text{Rs}\text{.}150\end{array}$$
And, B.G. = Rs. (165 - 150) = Rs. 15