A sum of Rs. 500 becomes Rs. 580 at simple interest in 2 years. In how many years will the sum of Rs. 660 amounts to Rs. 924 at the same rate of simple interest?

Correct option is B

Given:

A sum of Rs. 500 becomes Rs. 580 in 2 years at simple interest.

We have to find how many years it will take for Rs. 660 to amount to Rs. 924 at the same rate of simple interest.

Formula Used:

The formula for simple interest is:

​$$\text{Interest} = \frac{P \times R \times T}{100}$$  

A = P + SI
​

​$$A = P + \frac{P \times R \times T}{100}$$​​

Where:

A is the amount,

P is the principal,

R is the rate of interest per annum,

T is the time in years.​

Solution:

In the first case, Rs. 500 becomes Rs. 580 in 2 years. The interest earned is:

​$$\text{Interest} = 580 - 500 = 80$$​​​​

P = 500, $$\text{Interest}$$​ = 80, and T = 2:

​$$80 = \frac{500 \times R \times 2}{100}$$​​

​$$80 = \frac{1000R}{100} 80=10R80 = 10R R=8$$​​

So, the rate of interest is 8% per annum.

Now, we are given a new principal of Rs. 660, and the amount becomes Rs. 924

​$$\text{Interest} = 924 - 660 = 264$$​​

​$$\text{Interest} = \frac{660 \times 8 \times T}{100}$$​​

​$$264 = \frac{660 \times 8 \times T}{100}$$​​

​$$264 = \frac{5280T}{100}$$​​

264 = 52.8 T

T = $$\frac{264}{52.8} = 5$$​​

The time taken for Rs. 660 to amount to Rs. 924 is: 5 years

Thus, the correct option is (b) 5 years