A sum of money at a simple rate of interest $i_{1}$, doubles in 5 years. At another simple rate of interest $i_{2}$, it becomes three times in 12 years. Then, the two rates of interest $i_{1}$ and $i_{2}$ respectively are
(a)$10 \%, 16 \frac{2}{3} \%$
(b)10\%, 20\%
(c)20\%, $16 \frac{2}{3} \%$
(d)20\%, 30\%
Answer
Answer (as printed): C
Explanation
Case I. Let $\operatorname{sum}=₹ x$. Then, S.I. $=₹ x$. $\therefore \quad$ Rate $=\left(\frac{100 \times \text { S.I. }}{P \times T}\right)=\left(\frac{100 \times x}{x \times 5}\right) \%=20 \%$. Case II. Let sum $=₹ x$. Then, S.I. $=₹ 2 x$. ∴ $\quad$ Rate $=\left(\frac{100 \times \text { S.I. }}{P \times T}\right)=\left(\frac{100 \times 2 x}{x \times 12}\right) \%=\frac{50}{3} \%=16 \frac{2}{3} \%$.
Explanation as extracted from the printed page; notation may be imperfect.