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
(a)$5 \frac{1}{2}$ years
(b)$6 \frac{1}{2}$ years
(c)7 years
(d)$7 \frac{1}{2}$ years
Answer
Answer (as printed): D
Explanation
Let sum $=x$. Then, S.I. $=\frac{9}{16} x$. Let rate $=R \%$ and time $=R$ years. $$\therefore \quad\left(\frac{x \times R \times R}{100}\right)=\frac{9 x}{16} \Leftrightarrow R^{2}=\frac{900}{16} \Leftrightarrow R=\frac{30}{4}=7 \frac{1}{2} .$$ Hence, time $=7 \frac{1}{2}$ years.
Explanation as extracted from the printed page; notation may be imperfect.