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 interchanges the amount at the same rates, he earns Rs. 50 more. Find the amounts deposited by him at different rates.

Let the amount at 8% be x and the amount at 6% be y.

Where I is interest, P is the principal amount N is the time in years and R is the rate per annum.

Now,

I in case 1 of 8%

⇒ I = …[1]

in the second case of 6%

I = …[2]

The total interest is 500.

eq[1] + eq[2]

⇒

⇒ 4x + 3y = 25000 …[3]

Now if he interchanges the amount he gets 50 more

⇒

⇒ 4y + 3x = 27500 …[4]

Now, adding and subtracting equation eq[1] and eq[2].

7x + 7y = 52500

⇒ x + y = 7500 …[5]

x – y = –2500 …[6]

adding [5] and [6]

2x = 5000

⇒ x = 2500

and by [5]

x + y = 7500

⇒ 2500 + y = 7500

⇒ y = 5000