The banker's gain on a certain sum due $$1\frac{1}{2}$$ years hence is $$\frac{3}{{25}}$$ of the banker's discount. The rate percent is:

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let,}}\,{\text{B}}{\text{.D}}{\text{.}} = \operatorname{Rs} .\,{\kern 1pt} 1 \cr & {\text{Then,}}{\kern 1pt} \,{\text{B}}{\text{.G}}{\text{.}} = \operatorname{Re} .\,{\kern 1pt} \frac{3}{{25}} \cr & \therefore {\text{T}}{\text{.D}}{\text{. = }}\left( {{\text{B}}{\text{.D}}{\text{. - B}}{\text{.G}}{\text{.}}} \right) \cr & = \operatorname{Rs} .\,{\kern 1pt} \left( {1 - \frac{3}{{25}}} \right) \cr & = \operatorname{Rs} .{\kern 1pt} \,\frac{{22}}{{25}} \cr & {\text{Sum}} = {\frac{{1 \times {\frac{{22}}{{25}}} }}{{1 - {\frac{{22}}{{25}}} }}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}{\kern 1pt} \,\frac{{22}}{3} \cr & {\text{S}}{\text{.I}}{\text{.}}{\kern 1pt} \,{\text{on}}{\kern 1pt} {\text{Rs}}{\text{.}}\,{\kern 1pt} \frac{{22}}{3}{\kern 1pt} {\text{for}}\,{\kern 1pt} 1\frac{1}{2}\,{\text{years}}\,{\kern 1pt} {\text{is}}\,\operatorname{Rs} .\,{\kern 1pt} 1 \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 1}}{{\frac{{22}}{3} \times \frac{3}{2}}}} \right)\% {\kern 1pt} \cr & {\kern 1pt} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 9\frac{1}{9}\% \cr} $$