The banker's discount on a certain sum due 2 years hence is ¹¹/₁₀ of the true discount. The rate percent is:

Explanation:-

$$\eqalign{ & {\text{Let}}\,{\text{T}}{\text{.D}}{\text{.}}\,{\text{be}}\,{\text{Re}}{\text{.}}\,{\text{1}}{\text{.}} \cr & {\text{Then,}}\,{\text{B}}{\text{.D}}. = Rs.\,\frac{{11}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1.10. \cr & \therefore {\text{Sum}} = Rs.\,\left( {\frac{{1.10 \times 1}}{{1.10 - 1}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{110}}{{10}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,11. \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{11}}\,{\text{for}}\,{\text{2}}\,{\text{years}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{1}}{\text{.10}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 1.10}}{{11 \times 2}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \, \cr}$$