The simple interest on a sum for 5 years is `2/5` of the sum. The rate per cent per annum is

Options

A. `10%`
B. `8%`
C. `6%`
D. `12.1/2%`

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and the information provided in the question.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The simple interest (SI) for 5 years is \( \frac{2}{5} \) of the principal (P).
- Time (T) = 5 years.

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

3. **Substitute the Known Values into the Formula**:
- We know that \( SI = \frac{2}{5} P \) and \( T = 5 \).
- Substitute these values into the formula:
\[ \frac{2}{5} P = \frac{P \times 5 \times R}{100} \]

4. **Cancel the Principal (P)**:
- Since P is common on both sides, we can cancel it (assuming \( P \neq 0 \)):
\[ \frac{2}{5} = \frac{5R}{100} \]

5. **Cross-Multiply to Solve for R**:
- Cross-multiplying gives:
\[ 2 \times 100 = 5R \times 5 \]
\[ 200 = 25R \]

6. **Isolate R**:
- Divide both sides by 25:
\[ R = \frac{200}{25} \]
\[ R = 8 \]

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

### Final Answer:
The rate per cent per annum is **8%**.

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