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