Simple interest on a certain sum at a certain annual rate of interest is $\frac{1}{9}$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is
(a)$3 \frac{1}{3} \%$
(b)5\%
(c)$6 \frac{2}{3} \%$
(d)10\%
Answer
Answer (as printed): A
Explanation
Let sum $=x$. Then, S.I. $=\frac{x}{9}$. Let rate $=R \%$ and time $=R$ years. $$\therefore \quad\left(\frac{x \times R \times R}{100}\right)=\frac{x}{9} \Leftrightarrow R^{2}=\frac{100}{9} \Leftrightarrow R=\frac{10}{3}=3 \frac{1}{3} .$$ Hence, rate $=3 \frac{1}{3} \%$.
Explanation as extracted from the printed page; notation may be imperfect.