Finding the Rate of Interest

The problem provides information about the simple interest earned on two different principal amounts over the same period and the difference between these interests. We need to find the rate of interest per annum.

The formula for calculating Simple Interest (SI) is:

Where:

• \(P\) is the Principal amount
• \(R\) is the Rate of Interest per annum
• \(T\) is the Time period in years

We are given two scenarios:

1. Principal \(P_1 = \text{Rs. 1200}\)
2. Principal \(P_2 = \text{Rs. 1000}\)

The time period is the same for both cases, \(T = 3\) years.

Let the rate of interest be \(R\) percent per annum.

The simple interest earned on Rs. 1200 in 3 years at rate \(R\) is:

The simple interest earned on Rs. 1000 in 3 years at rate \(R\) is:

We are told that the interest on Rs. 1200 is more than the interest on Rs. 1000 by Rs. 120. This means the difference between \(SI_1\) and \(SI_2\) is Rs. 120.

Substitute the expressions for \(SI_1\) and \(SI_2\):

Combine the terms involving \(R\):

Now, solve for \(R\):

So, the rate of interest per annum is 20 percent.

Let's verify this rate:

• Interest on Rs. 1200 at 20% for 3 years: \( \frac{1200 \times 20 \times 3}{100} = \frac{72000}{100} = 720 \)
• Interest on Rs. 1000 at 20% for 3 years: \( \frac{1000 \times 20 \times 3}{100} = \frac{60000}{100} = 600 \)

The difference in interest is \(720 - 600 = 120\), which matches the information given in the problem. Therefore, the rate of interest is indeed 20 percent.

The final answer is 20 percent.