Question

Sonal invests money in three different schemes for $5$ years, $10$ years and $12$ years at $10\%$ p.a., $12\%$ p.a. and $15\%$ p.a. at simple interest respectively. At the completion of each scheme, she gets the same interest. What is the ratio of her investments?

• A. $36:15:10$
• B. $3:2:1$
• C. $3:4:5$
• D. $2:3:6$

Answer 1

The correct option is A $36:15:10$

Suppose, Sonal invests Rs. a,b,c at 10$\%$p.a,12$\%$p.a, 15$\%$p.a for 5 years, 10 years & 12 years at simple interest respectively.

Interest earned on an investment of Rs. a at $10\%$ p.a for 5 years$=I_a=\frac{a\times 10\times 5}{100}=\frac{a}{2}$

Interest earned on an investment of Rs. b at $12\%$ p.a for 10 years$=I_b=\frac{b\times 12\times 10}{100}=\frac{6b}{5}$

Interest earned on an investment of Rs. c at $15\%$ p.a for 15 years$=I_c=\frac{c\times 15\times 12}{100}=\frac{9c}{5}$

Given $I_a=I_b=I_c$

$\Rightarrow \frac{a}{2}=\frac{6b}{5}=\frac{9c}{5}$

$\Rightarrow 5a=12b=18c$

$\Rightarrow \frac{a}{\frac{1}{5}}=\frac{b}{\frac{1}{12}}=\frac{c}{\frac{1}{18}}$

$\therefore$The investment should be made in the ratio$=a:b:c$

$\Rightarrow \frac{1}{5}:\frac{1}{12}:\frac{1}{18}=36:15:10$