The banker's discount on a sum of money for 3 years is Rs. 1116. The true discount on the same sum for 4 years is Rs. 1200. What is the rate per cent?

Solution(By Examveda Team)

$$\eqalign{ & BD\,{\text{for}}\,3\,{\text{years}} = {\text{Rs}}{\text{.}}\,1116 \cr & BD\,{\text{for}}\,4\,{\text{years}} = \frac{{1116}}{3} \times 4 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}1488 \cr & TD\,{\text{for}}\,4\,{\text{years}} = {\text{Rs}}{\text{.}}\,1200 \cr & F = \frac{{BD \times TD}}{{BD - TD}} \cr & \,\,\,\,\,\,\, = \frac{{1488 \times 1200}}{{1488 - 1200}} \cr & \,\,\,\,\,\,\, = \frac{{1488 \times 1200}}{{288}} \cr & \,\,\,\,\,\,\, = \frac{{124 \times 1200}}{{24}} \cr & \,\,\,\,\,\,\, = \frac{{124 \times 100}}{2} \cr & \,\,\,\,\,\,\, = 62 \times 100 \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,6200 \cr} $$
⇒ Rs. 1488 is the simple interest on Rs. 6200 for 4 years
$$\eqalign{ & \Rightarrow 1488 = \frac{{6200 \times 4 \times R}}{{100}} \cr & \Rightarrow R = \frac{{1488 \times 100}}{{6200 \times 4}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{372 \times 100}}{{6200}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{372}}{{62}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\% \cr} $$