If ratio of principal and simple interest for 1 year is 25 : 1, then the rate of interest is

Options

A. 0.04
B. 0.25
C. 0.05
D. 0.2

Answer

To find the rate of interest when the ratio of principal to simple interest for 1 year is given as 25:1, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**:
The ratio of principal (P) to simple interest (SI) is given as 25:1. This means:
\[ \frac{P}{SI} = \frac{25}{1} \]
From this, we can express simple interest in terms of principal:
\[ SI = \frac{P}{25} \]

2. **Use the Simple Interest Formula**:
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( R \) is the rate of interest and \( T \) is the time in years. Since we are considering 1 year, we can substitute \( T = 1 \):
\[ SI = \frac{P \times R \times 1}{100} = \frac{P \times R}{100} \]

3. **Set the Two Expressions for Simple Interest Equal**:
Now we can equate the two expressions for simple interest:
\[ \frac{P}{25} = \frac{P \times R}{100} \]

4. **Eliminate P from the Equation**:
Assuming \( P \neq 0 \), we can divide both sides by \( P \):
\[ \frac{1}{25} = \frac{R}{100} \]

5. **Cross-Multiply to Solve for R**:
Cross-multiplying gives us:
\[ 100 = 25R \]

6. **Solve for R**:
Dividing both sides by 25:
\[ R = \frac{100}{25} = 4 \]

7. **Conclusion**:
Therefore, the rate of interest is:
\[ R = 4\% \]