Question

A person invested some amount at the rate of 12% simple interest and the remaining at 10%. He received yearly an interest of Rs 130. Had he interchanged the amounts invested, he would have received an interest of Rs 134. How much money did he invest at different rates?

• A. Rs 500 at the rate of 10%, Rs 800 at the rate of 12%
• B. Rs 700 at the rate of 10%, Rs 600 at the rate of 12%
• C. Rs 800 at the rate of 10%, Rs 400 at the rate of 12%
• D. Rs 700 at the rate of 10%, Rs 500 at the rate of 12%
• E. None of these

Answer 1

The correct option is D

Rs 700 at the rate of 10%, Rs 500 at the rate of 12%

Let the person invest Rs x and y at two different rates 12% and 14% respectively.
$\therefore \frac{x\times 12\times 1}{100}+\frac{y\times 10\times 1}{100}=130(\because SI=\frac{P\times R\times T}{100})\Rightarrow 12x+10y=13000...\left(i\right)$
After inter-changing invested amount,
$\frac{y\times 12\times 1}{100}+\frac{x\times 10\times 1}{100}=134\Rightarrow 12y+10x=13400\left(ii\right)$
On solving equations (i) and (ii), we get
x = Rs 500 and y = Rs 700