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 amount. What is the ratio of his investments?

• A. $6:3:2$
• B. $2:3:4$
• C. $3:4:6$
• D. $77:56:44$

Answer 1

The correct option is D $77:56:44$

Let the investment of A, B & C be $P_1,P_2,P_3$ respectively.
According to the question.
$P_1+\frac{P_1\times 10\times 6}{100}=P_2+\frac{P_2\times 12\times 10}{100}=P_3+\frac{P_3\times 15\times 12}{100}$
$\frac{10P_1+6P_1}{10}=\frac{10P_2+12P_2}{10}=\frac{10P_3+18P_3}{10}$
$16P_1=22P_2=28P_3$
$P_1=\frac{k}{16},P_2=\frac{k}{22},P_3=\frac{k}{28}$
LCM of $16,22$ & $28$ is $1232$.
$P_1:P_2:,P_3=\frac{k}{16}\times 1232:\frac{k}{22}\times 1232:\frac{k}{28}\times 1232$
= $77:56:44$