Amit invests a sum of ₹5400 and Gopal invests a sum of ₹9400 at the same rate of simple interest per annum. If, at the end of 4 years, Gopal gets ₹480 more interest than Amit, then find the rate of interest per annum (in percentage).

Correct option is B

Given:

Amit invests ₹5400.

Gopal invests ₹9400.

The time period for both investments is 4 years.

Gopal's interest is ₹480 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:

​$$\text{SI}_A = \frac{5400 \times R \times 4}{100} = \frac{21600R}{100} = 216R$$​​

For Gopal:

​$$\text{SI}_G = \frac{9400 \times R \times 4}{100} = \frac{37600R}{100} = 376R$$​​

The difference in interest between Gopal and Amit is ₹480:

​$$\text{SI}_G - \text{SI}_A = 480$$​​

376R - 216R = 480

160R = 480

​$$R = \frac{480}{160} = 3$$​​

Thus, the rate of interest per annum is 3%.