Question

A person invests money in three different schemes for $6$ years, $10$ years and $12$ years at $10\%,12\%$ and $15\%$ simple interest respectively. At the completion of each scheme, he gets the same interest. What is the ratio of his investments?

• A. $6:3:2$.
• B. $2:3:4$.
• C. $5:2:1$.
• D. $7:4:2$.

Answer 1

Answer: (A)

$6:3:2$.

Let the required ratio be $x:y:z$. Then,
S.I. on Rs. $x$ for $6$ years at $10\%$ p.a. $=$ S.I. on Rs. $y$ for $10$ years at $12\%$ p.a.
$\Rightarrow \frac{x\times 6\times 10}{100}=\frac{y\times 10\times 12}{100}\Rightarrow \frac{x}{y}=\frac{2}{1}$

S.I. on Rs. $y$ for $10$ years at $12\%$ p.a. $=$ S.I. on Rs. $z$ for $12$ years at $15\%$ p.a.
$\Rightarrow \frac{y\times 10\times 12}{100}=\frac{z\times 12\times 15}{100}\Rightarrow \frac{y}{z}=\frac{3}{2}$
$\Rightarrow x:y=2:1$ and $y:z=3:2$
$\Rightarrow x:y=6:3$ and $y:z=3:2$
$\Rightarrow x:y:z=6:3:2$.