Question

A man has rs.1900. He lent some of it at 5% pa and rest at 9% pa. The total amount of interest he got after 4 yrs was rs.580.What was the sum?

Answer 1

Amount lent @ 9% Interest = Rs 1250 and amount lent at 5% Interest = Rs 650.

Explanation:

Taking it as simple Interest:

`I =( P N R) / 100`

Let x be the amount lent @ 9% Interest.

Then 1900 - x is the amount lent at 5% Interest.

`I = Rs 580, N = 4 years`

`(x * 4 * 9)/ 100 + ((1900-x) * 4 * 5)/100 = 580`

`36 x + 38000 - 20x = 58000`

`16 x = 58000 - 38000 = 20000`

`x = 20000/16 = Rs 1250`

`1900 - x = 1900 - 1250 = Rs 650`

Answer 2

Amount lent @ 9% Interest = Rs 869.71 and amount lent @ 5% is = Rs 1030.29

Explanation:

Taking it as compound interest.

`A = P (1 + R/100)^`

Let x be the amount lent at 9% Interest.

Then 1900 - x is the amount lent @ 5% Interest.

`P = 1900, I = 580, N = 4 years`

`1900 + 580 = x (1 + 9/100)^4 + (1900-x) (1 + 5/100)^4`

`x 1.09^4 + 1900 * 1.05^4 - x 1.05^4 = 2480`

`1.4116 x - 1.2155x = 2480 - 1900* 1.2155 = 170.55`

`x = 170.55 / (1.4116 - 1.2155) = 869.71`

`1900 - x = 1900 - 869.71 = 1030.29`