The banker's discount on a sum of money for $$1\frac{1}{2}$$ years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:

Solution(By Examveda Team)

$$\eqalign{ & {\text{B}}{\text{.D}}{\text{.}}\,{\text{for}}\frac{3}{2}{\text{years}} = Rs.\,558 \cr & {\text{B}}{\text{.D}}{\text{.}}\,{\text{for 2}}\,{\text{years}} \cr & = Rs.\left( {558 \times \frac{2}{3} \times 2} \right) \cr & = Rs.\,744 \cr & {\text{T}}{\text{.D}}{\text{.}}\,{\text{for}}\,{\text{2}}\,{\text{years}} = Rs.\,600 \cr & \therefore {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{744 \times 600}}{{144}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3100 \cr & {\text{Thus,}}\,{\text{Rs}}{\text{.}}\,{\text{744}}\,{\text{is}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{3100}}\,{\text{for}}\,{\text{2}}\,{\text{years}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 744}}{{3100 \times 2}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$