Question

A sum of money at simple interest amounts to rs.2800 in 2 years and rs.3250 in 5 years. Find the sum and the rate of interest.

Answer 1

Answer:

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

Step-by-step explanation:

Given:

Amount in 2 years = Rs. 2800

Amount in 5 years = Rs. 3250

To find: Principal and rate of interest.

We know that,

$SI=\frac{P\times R\times T}{100}$

A = P + SI

SI = A - P

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

According to the Question,

$2800-P=\frac{P\times R\times2}{100}$

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

$3250-P=\frac{P\times R\times5}{100}$

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

Divide (2) by (1),

$\frac{140000-50P}{65000-20P}=\frac{PR}{PR}$

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%.