Question

An employee deposits certain amount at the rate of $8\%$ per annum and a certain amount at the rate of $6\%$ per annum at simple interest. He earns $Rs.500$ as annual interest. If he interchange the amount at the same rates, he earns $Rs.50$ more. Find amount deposited by him at different rate.

Answer 1

For amount $x$,

Rate of interest $r=8$%, Time $,t=1year$

For amount $y$,

Rate of interest $r=6$%, Time $,t=1year$

Let's suppose, Deposited amounts are $xandy$

Simple Interest $=\frac{Principal\times amount\times r\times t}{100}$

Then,

It is given that

$\frac{x\times 8}{100}+\frac{y\times 6}{100}=500$

$(4x+3y=25000)$ .....(1)

When amount are interchanged, he earns $Rs.50$ more,

$\frac{x\times 6}{100}+\frac{y\times 8}{100}=500+50$

$3x+4y=27500$ .....(2)

Equation $\left(2\right)$ is multiplied by $4$ and equation $\left(1\right)$ is multiplied by $3$

$12x+16y=110000$ .........(3)

$12x+9y=75000$ .........(4)

On subtracting equation(4) from equation$\left(3\right)$, we get

$7y=35000$

$y=5000$ substituting this value in equation $\left(1\right)$,

$4x+3\times 5000=25000$

$x=2500$.

Hence, an employee deposits $Rs.2500$ at the rate of $8$% per annum and $Rs.5000$ at the rate of $6$% per annum at simple interest.