Question

A person invested some amount at the rate of $12\%$ simple interest and some other amount at the rate of $10$ $\%$ simple interest. He received yearly interest of Rs. $130$. If he had interchanged the amounts invested he would have received Rs. $4$ more as interest. How much amount did he invest at different rates?

• A. Rs. $500$ at $12\%$, Rs. $700$ at $10\%$
• B. Rs. $700$ at $12\%$, Rs. $500$ at $10\%$
• C. Rs. $800$ at $12\%$, Rs. $500$ at $10\%$
• D. None of these

Answer 1

The correct option is A Rs. $500$ at $12\%$, Rs. $700$ at $10\%$

Given: Person invested $X$ amount at rate of $12$ $\%$
and $Y$ amount at rate of $10$ $\%$
Yearly interest received $=$ Rs. $130$
If investment is interchanged i.e $X$ amount at $10$ $\%$ and
Y amount at $12$ $\%$
Total interest received $=$ Rs. $134$
To calculate : $X$ and $Y$ .
Solution:
$\frac{12}{100}\times X+\frac{10}{100}\times Y=130$ ....Equation.1
$\frac{10}{100}\times X+\frac{12}{100}\times Y=134$ ....Equation.2
Multiplying Equation (1) by $5$ and Equation (2) by $6$, we get
$0.6X+0.5Y=650$ ....Equation 3.
$0.6X+0.72Y=804$ ....Equation 4.
Subtracting new equation, we get
$(0.72-0.5)Y=154$
$Y=700$
On substituting in Equation (3),
$0.6X=650-350$
$X=500$
He invested: $Rs.500$ at $12$% and $Rs.700$ at $10$ $\%$.