The true discount on a certain sum due 6 months hence at 15% is Rs. 240. What is the banker's discount on the same sum for the same time at the same rate?

$$\eqalign{ & TD = {\text{Rs}}{\text{.}}\,240 \cr & T = 6\,{\text{months}}\, = \frac{1}{2}\,{\text{year}} \cr & R = 15\% \cr & TD = \frac{{BG \times 100}}{{TR}} \cr & \Rightarrow 240 = \frac{{BG \times 100}}{{\left( {\frac{1}{2} \times 15} \right)}} \cr & BG = \frac{{240 \times 15}}{{100 \times 2}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{120 \times 15}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,18 \cr & BG = BD - TD \cr & \Rightarrow 18 = BD - 240 \cr & \Rightarrow BD = 18 + 240 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,258 \cr} $$