A sum of money at Simple Interest amounts to Rs.2800 in 2 years and Rs.3250 in 5 years. Findthe sum and the rate of interest.

Given:

Amount in 2 years = Rs. 2800

Amount in 5 years = Rs. 3250

To find: Principal and rate of interest.

We know that,

A = Total Accrued Amount (principal + interest)

A = P + SI

SI = A - P

let, P be the principal and R is the rate of interest.

According to the Question,

A=P+ $$SI =\frac{ P \times(R) \times T }{ 100}$$

Amount in 2 years = Rs. 2800

$$2800=\frac{ P \times(R) \times 2 }{ 100}$$

140000 - 50P = PR ............................(1)

Amount in 5 years = Rs. 3250

A=P+ $$SI =\frac{ P \times(R) \times T }{ 100}$$

$$3250=\frac{ P \times(R) \times 5 }{ 100}$$

65000 - 20P = PR ............................(2)

Divide (2) by (1),

140000 - 50P = 65000 - 20P

50P - 20P = 140000 - 65000

30P = 75000

P = 2500

Put this value of P in (1),

140000 - 50(2500) = 2500R

2500R = 140000 - 125000

2500R = 15000

R = 6

Therefore, The sum is Rs. 2500 and rate of interest is 6%.