On a certain sum, the simple interset at the end of `6(1)/(4)` years becomes `(3)/(8)` of the sum. The rate of interset is

Options

A. 0.05
B. 0.06
C. 0.07
D. 0.08

Answer

To solve the problem step by step, we will follow the information given in the question and apply the formula for simple interest.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- We are given that the simple interest (SI) at the end of \(6 \frac{1}{4}\) years is \(\frac{3}{8}\) of the principal (P).
- We need to find the rate of interest (R).

2. **Convert the Time into Improper Fraction:**
- The time given is \(6 \frac{1}{4}\) years.
- Convert this mixed number into an improper fraction:
\[ 6 \frac{1}{4} = \frac{25}{4} \text{ years} \]

3. **Use the Simple Interest Formula:**
- The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Here, \(SI = \frac{3}{8}P\) and \(T = \frac{25}{4}\).

4. **Substitute the Values into the Formula:**
- Substitute \(SI\) and \(T\) into the simple interest formula:
\[ \frac{3}{8}P = \frac{P \times R \times \frac{25}{4}}{100} \]

5. **Cancel the Principal (P) from Both Sides:**
- Since \(P\) is common on both sides, we can cancel it out:
\[ \frac{3}{8} = \frac{R \times \frac{25}{4}}{100} \]

6. **Rearrange the Equation to Solve for R:**
- Multiply both sides by 100 to eliminate the fraction:
\[ 100 \times \frac{3}{8} = R \times \frac{25}{4} \]
- This simplifies to:
\[ \frac{300}{8} = R \times \frac{25}{4} \]
- Further simplify \(\frac{300}{8}\):
\[ \frac{300}{8} = 37.5 \]
- Now we have:
\[ 37.5 = R \times \frac{25}{4} \]

7. **Isolate R:**
- To isolate \(R\), multiply both sides by \(\frac{4}{25}\):
\[ R = 37.5 \times \frac{4}{25} \]
- Calculate \(R\):
\[ R = \frac{150}{25} = 6 \]

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

### Final Answer:
The rate of interest is \(6\%\) per annum.