Amit invests a sum of Rs. 5400 and Gopal invests a sum of Rs. 10200 at the same rate of simple interest per annum. If, at the end of 4 years, Gopal gets Rs. 960 more interest than Amit, then find the rate of interest per annum (in percentage).

Correct option is B

Given:

Amit invests ₹5400.

Gopal invests ₹10200.

The time period for both investments is 4 years.

Gopal's interest is ₹960 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:

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

For Gopal:

​$$\text{SI}_G = \frac{10200 \times R \times 4}{100} \\$$​​

The difference in interest between Gopal and Amit is ₹960

$$\frac{(10200-5400)\times R \times 4}{100}=960 \\\ \\\Rightarrow \frac{4800\times4R}{100}=960 \\\ \\\Rightarrow 192R=960 \\\ \\\Rightarrow R=5\% \\\ \\$$​