What is the difference between the banker's discount and the true discount on Rs. 8100 for 3 months at 5%

Solution(By Examveda Team)

$$\eqalign{ & F = {\text{Rs}}{\text{.}}\,8100 \cr & R = 5\% \cr & T = 3\,{\text{months}} = \frac{1}{4}\,{\text{years}} \cr & BD = \frac{{FTR}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{8100 \times \frac{1}{4} \times 5}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2025}}{{20}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{405}}{4} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{ Rs}}{\text{.}}\,101.25 \cr & TD = \frac{{FTR}}{{100 + (TR)}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{8100 \times \frac{1}{4} \times 5}}{{100 + \left( {\frac{1}{4} \times 5} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{2025 \times 5}}{{100 + \left( {\frac{5}{4}} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{2025 \times 5 \times 4}}{{400 + 5}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{2025 \times 5 \times 4}}{{405}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{405 \times 5 \times 4}}{{81}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{45 \times 5 \times 4}}{9} \cr & \,\,\,\,\,\,\,\,\,\,\, = 5 \times 5 \times 4 \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,100 \cr & BD - TD = \,101.25 - 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1.25 \cr} $$