If the interest on Rs. 800 be more than the interest on Rs. 400 by Rs. 40 in 2 years, then find the rate of interest per annum.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We need to find the rate of interest per annum (r) given that the interest on Rs. 800 is more than the interest on Rs. 400 by Rs. 40 in 2 years.

### Step 2: Write the Formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Calculate the Simple Interest for Rs. 800
For the principal amount of Rs. 800:
\[ SI_{800} = \frac{800 \times R \times 2}{100} = \frac{1600R}{100} = 16R \]

### Step 4: Calculate the Simple Interest for Rs. 400
For the principal amount of Rs. 400:
\[ SI_{400} = \frac{400 \times R \times 2}{100} = \frac{800R}{100} = 8R \]

### Step 5: Set Up the Equation
According to the problem, the interest on Rs. 800 is more than the interest on Rs. 400 by Rs. 40. Therefore, we can write the equation:
\[ SI_{800} - SI_{400} = 40 \]
Substituting the values we calculated:
\[ 16R - 8R = 40 \]

### Step 6: Simplify the Equation
Now, simplify the equation:
\[ 8R = 40 \]

### Step 7: Solve for R
To find the rate of interest \( R \):
\[ R = \frac{40}{8} = 5 \]

### Step 8: Conclusion
The rate of interest per annum is:
\[ \text{Rate} = 5\% \]