In how many years will a sum of money put at simple interest treble itself ? I. The interest earned in 4 years is half the sum. 1 II. The rate of interest is 12 %. 2 III. The sum doubles itself in 8 years at simple interest.
(a)Any one of the three
(b)Any two of the three
(c)All I, II and III
(d)II and III only
(e)I and II only
Answer
Answer (as printed): A
Explanation
Let sum be ₹ $x$. Then, S.I. $=₹(3 x-x)=₹ 2 x, T=$ ? I. gives : When $T=4$, then $\therefore \quad R=\frac{100 \times \text { S.I. }}{P \times T}=\left(100 \times \frac{x}{2} \times \frac{1}{x} \times \frac{1}{4}\right)=12 \frac{1}{2} \%$ p.a. Now, Sum $=₹ x$, S.I. $=₹ 2 x, T=$ ? $\therefore \quad T=\frac{100 \times \text { S.I. }}{P \times R}=\left(\frac{100 \times 2 x}{x \times 25} \times 2\right)=16$ years. Thus, $I$ only gives the answer. II. gives, $R=\frac{25}{2} \%$ p.a. $\therefore \quad T=\frac{100 \times \text { S.I. }}{P \times R}=\left(\frac{100 \times 2 x}{x \times 25} \times 2\right)=16$ years. Thus, II only also gives the answer. III. gives, $R=5 \%$ p.a. $\therefore \quad T=\frac{100 \times \text { S.I. }}{P \times R}=\left(\frac{100 \times 2 x}{x \times 5}\right)=40$ years Thus, III only also gives the answer. ∴ Correct answer is (a).
Explanation as extracted from the printed page; notation may be imperfect.