If Rs. 4 becomes Rs. 10 in 50 years at simple interest, the rate % p.a. is

Options

A. 5%
B. 2.5%
C. 3%
D. 3.5%

Answer

To find the rate of interest per annum, we can use the formula for simple interest. The formula for calculating simple interest is:

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- SI = Simple Interest
- P = Principal amount (initial amount)
- R = Rate of interest per annum
- T = Time (in years)

### Step-by-Step Solution:

1. **Identify the values**:
- Principal (P) = Rs. 4
- Amount (A) after 50 years = Rs. 10
- Time (T) = 50 years

2. **Calculate the Simple Interest (SI)**:
- The formula for the amount (A) is:
\[ A = P + \text{SI} \]
- Rearranging gives:
\[ \text{SI} = A - P \]
- Substitute the values:
\[ \text{SI} = 10 - 4 = 6 \text{ Rs.} \]

3. **Substitute the known values into the SI formula**:
- We know:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
- Substitute SI, P, and T:
\[ 6 = \frac{4 \times R \times 50}{100} \]

4. **Simplify the equation**:
- Multiply both sides by 100 to eliminate the fraction:
\[ 600 = 4 \times R \times 50 \]
- Simplify the right side:
\[ 600 = 200R \]

5. **Solve for R**:
- Divide both sides by 200:
\[ R = \frac{600}{200} = 3 \]

6. **Conclusion**:
- The rate of interest per annum (R) is 3%.

### Final Answer:
The rate of interest per annum is **3%**.