Amit invests a sum of ₹5400 and Gopal invests a sum of ₹9400 at the same rate ofsimple interest per annum. If, at the end of 6 years, Gopal gets ₹960 more interest thanAmit, then find the rate of interest per annum (in percentage).

Correct option is C

Given:​

Amit's investment = ₹5400

Gopal's investment = ₹9400

Time period = 6 years

Gopal gets ₹960 more interest than Amit.

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

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

where P is the principal, R is the rate of interest, and T is the time in years.

Solution:

The interest for Amit and Gopal can be written as:

Interest of Amit = $$\frac{5400 \times R \times 6}{100}$$​​

Interest of Gopal = $$\frac{9400 \times R \times 6}{100}$$​​

The difference in interest is:

​$$\frac{9400 \times R \times 6}{100} - \frac{5400 \times R \times 6}{100} = 960$$​​

​$$6R \times \left( \frac{9400 - 5400}{100} \right) = 960$$​​

​$$6R \times \left( \frac{4000}{100} \right) = 960$$​​

​$$6R \times 40 = 960$$​​

240R = 960

​$$R = \frac{960}{240} = 4$$​​

Thus, the rate of interest per annum is 4%