A sum of money lent out at compound interest increases in value by 50\% in 5 years. A person wants to lend three different sums $x, y$ and $z$ for 10, 15 and 20 years respectively at the above rate in such a way that he gets back equal sums at the end of their respective periods. The ratio $x: y: z$ is
(a)6 : 9 : 4
(b)9 : 4 : 6
(c)9 : 6 : 4
(d)6 : 4 : 9
Answer
Answer (as printed): C
Explanation
$P\left(1+\frac{R}{100}\right)^{5}=150 \%$ of $P=\frac{3}{2} P \Rightarrow\left(1+\frac{R}{100}\right)^{5}=\frac{3}{2}$. $$\begin{aligned} & x\left(1+\frac{R}{100}\right)^{10}=y\left(1+\frac{R}{100}\right)^{15}=z\left(1+\frac{R}{100}\right)^{20} \\ \Rightarrow & x\left\{\left(1+\frac{R}{100}\right)^{5}\right\}^{2}=y\left\{\left(1+\frac{R}{100}\right)^{5}\right\}^{3}=z\left\{\left(1+\frac{R}{100}\right)^{5}\right\}^{4} \\ \Rightarrow & x \times\left(\frac{3}{2}\right)^{2}=y \times\left(\frac{3}{2}\right)^{3}=z \times\left(\frac{3}{2}\right)^{4} \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.