Question
Simple interest on a certain amount is $$\frac{9}{{16}}$$ of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is -
Answer: Option D
$$\eqalign{
& {\text{Let}}\,{\text{sum}} = x. \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = \frac{{\text{9}}}{{{\text{16}}}}x \cr
& {\text{Let rate}} = {\text{R}}\% \,\text{and} \cr
& \text{time} = R\,\text{years} \cr
& \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{{9x}}{{16}} \cr
& \Rightarrow {{\text{R}}^2} = \frac{{900}}{{16}} \cr
& {\text{R}} = \frac{{30}}{4} = 7\frac{1}{2} \cr
& {\text{Hence,}} \cr
& {\text{time}} = 7\frac{1}{2}\text{years} \cr} $$
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$$\eqalign{
& {\text{Let}}\,{\text{sum}} = x. \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = \frac{{\text{9}}}{{{\text{16}}}}x \cr
& {\text{Let rate}} = {\text{R}}\% \,\text{and} \cr
& \text{time} = R\,\text{years} \cr
& \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{{9x}}{{16}} \cr
& \Rightarrow {{\text{R}}^2} = \frac{{900}}{{16}} \cr
& {\text{R}} = \frac{{30}}{4} = 7\frac{1}{2} \cr
& {\text{Hence,}} \cr
& {\text{time}} = 7\frac{1}{2}\text{years} \cr} $$
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