Question

A man invested an amount at 10% per annum simple interest and another amount at 8% per annum simple interest. He received an annual interest of Rs. 1350. But, if he had interchanged the amounts invested, he would have received Rs. 45 less. What amounts did he invest at different rates?

A man invested an amount at 10% per annum and another amount at 8% per annum simple interest. Thus, he received ₹ 1350 as annual interest. Had he interchanged the amounts invested, he would have received ₹ 45 less as interest. What amounts did he invest at different rates?

Answer 1

Let the amounts invested at 10% and 8% be Rs. x and Rs. y respectively.

Then as per the question

`(x xx 10 xx 1)/100 = (y xx 8 xx 1)/100 = 1350`

10x + 8y = 135000   ...(i)

After the amounts interchanged but the rate being the same, we have

`(x xx 8 xx 1)/100 = (y xx 10 xx 1)/100 = 1350 - 45`

8x + 10y = 130500   ...(ii)

Adding (i) and (ii) and dividing by 9, we get

2x + 2y = 29500   ...(iii)

Subtracting (ii) from (i), we get

2x – 2y = 4500

Now, adding (iii) and (iv), we have

4x = 34000

`x = 34000/4`

x = 8500

Putting x = 8500 in (iii), we get

2 × 8500 + 2y = 29500

2y = 29500 – 17000

2y = 12500

`y = 12500/2` 

y = 6250

Hence, the amounts invested are Rs. 8,500 at 10% and Rs. 6,250 at 8%.