Amit invests a sum of Rs. 5400 and Gopal invests a sum of Rs. 9400 at the same rate of simple interest per annum. If, at the end of 5 years, Gopal gets Rs. 600 more interest than Amit, then find the rate of interest per annum (in percentage).

Correct option is A

Given:

Amit invests ₹5400.

Gopal invests ₹9400.

The time period for both investments is 5 years.

Gopal's interest is ₹600 more than Amit's interest.

Formula Used:
The formula for Simple Interest (SI) is:

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

where:

P is the principal amount,

R is the rate of interest per annum,

T is the time in years.

Solution:

For Amit:

​$$\text{SI}_A = \frac{5400 \times R \times 5}{100} = \frac{27000R}{100} = 270R$$​​

For Gopal:

​$$\text{SI}_G = \frac{9400 \times R \times 4}{100} = \frac{47000R}{100} = 470R$$​​

The difference in interest between Gopal and Amit is ₹600:

​$$\text{SI}_G - \text{SI}_A = 600$$​​

470R - 270R = 600

200R = 600

​$$R = \frac{600}{200} = 3$$%