The simple interest on a sum of money for 5 years is `3/5` of the sum. Find the rate per cent per annum.

Answer

To solve the problem step by step, we will use the information provided in the question and the formula for simple interest.

### Step-by-Step Solution:

1. **Understand the Problem**:
- We are given that the simple interest (SI) for 5 years is \( \frac{3}{5} \) of the principal (sum of money).
- We need to find the rate of interest per annum.

2. **Define Variables**:
- Let the principal (sum of money) be \( X \).
- Therefore, the simple interest (SI) can be expressed as:
\[ SI = \frac{3}{5} X \]

3. **Use the Simple Interest Formula**:
- The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Where:
- \( P \) = Principal (which is \( X \))
- \( R \) = Rate of interest per annum (which we need to find)
- \( T \) = Time in years (which is 5 years)

4. **Substitute Known Values into the Formula**:
- Substitute \( SI \), \( P \), and \( T \) into the formula:
\[ \frac{3}{5} X = \frac{X \times R \times 5}{100} \]

5. **Simplify the Equation**:
- Cancel \( X \) from both sides (assuming \( X \neq 0 \)):
\[ \frac{3}{5} = \frac{R \times 5}{100} \]

6. **Cross-Multiply to Solve for \( R \)**:
- Cross-multiplying gives:
\[ 3 \times 100 = 5 \times R \times 5 \]
\[ 300 = 25R \]

7. **Isolate \( R \)**:
- Divide both sides by 25:
\[ R = \frac{300}{25} \]
\[ R = 12 \]

8. **Conclusion**:
- The rate of interest per annum is:
\[ R = 12\% \]