The true discount on a certain of money due $${\text{2}}\frac{{\text{2}}}{{\text{3}}}$$ years hence, is Rs. 150 and the simple interest on the same sum for the same time and at the same rate is Rs. 200. Interest rate per annum is ?

$$\eqalign{ & {\text{True}}\,{\text{Discount}}\, = \,{\text{Rs}}{\text{. 150}} \cr & {\text{and}} \cr & {\text{Simple}}\,{\text{interest}}\, = \,{\text{Rs}}{\text{.}}\,{\text{200}} \cr & {\text{Sum}}\,{\text{due}}\, = \,\frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{TD}}}}{{\left( {{\text{S}}{\text{.I}}{\text{.}}} \right) - \left( {{\text{TD}}} \right)}} \cr & = \,{\text{Rs}}{\text{.}}\left( {\frac{{200 \times 150}}{{200 - 150}}} \right) \cr & = \,{\text{Rs}}. 600 \cr & \therefore {\text{Rate}} \cr & \, = \,\left( {\frac{{100 \times 200}}{{600 \times \frac{8}{3}}}} \right)\% \cr & = \,\left( {\frac{{20000}}{{1600}}} \right)\% \cr & = \,\left( {\frac{{200}}{{16}}} \right)\% \cr & = \,12\frac{1}{2}\% \cr} $$