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

Options

A. `5%`
B. `5(1)/(2)%`
C. `6%`
D. None of these

Answer

To solve the problem, we need to find the rate of interest per annum (R) given that the simple interest on Rs. 800 is more than the interest on Rs. 400 by Rs. 40 over a period of 2 years.

### Step-by-Step Solution:

1. **Identify the given values**:
- Principal for the first case (P1) = Rs. 800
- Principal for the second case (P2) = Rs. 400
- Time (T) = 2 years
- Difference in interest = Rs. 40

2. **Write the formula for Simple Interest (SI)**:
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where P is the principal, R is the rate of interest per annum, and T is the time in years.

3. **Calculate the Simple Interest for both principals**:
- For Rs. 800:
\[ SI_1 = \frac{800 \times R \times 2}{100} = \frac{1600R}{100} = 16R \]
- For Rs. 400:
\[ SI_2 = \frac{400 \times R \times 2}{100} = \frac{800R}{100} = 8R \]

4. **Set up the equation based on the problem statement**:
According to the problem, the interest on Rs. 800 is Rs. 40 more than the interest on Rs. 400:
\[ SI_1 = SI_2 + 40 \]
Substituting the values we calculated:
\[ 16R = 8R + 40 \]

5. **Solve for R**:
Rearranging the equation:
\[ 16R - 8R = 40 \]
\[ 8R = 40 \]
Dividing both sides by 8:
\[ R = \frac{40}{8} = 5 \]

6. **Conclusion**:
The rate of interest per annum is:
\[ R = 5\% \]

### Final Answer:
The rate of interest per annum is **5%**.

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