At what rate per cent annum will the simple interset on a sum of money of `(2)/(5)` of the amount in 10 years ?

Options

A. 0.04
B. 0.06
C. `5(2)/(3) %`
D. `6(2)/(3) %`

Answer

To solve the problem step by step, we need to find the rate of interest per annum when the simple interest on a sum of money is \( \frac{2}{5} \) of the principal amount in 10 years.

### Step-by-Step Solution

1. **Understand the Given Information:**
- Simple Interest (SI) = \( \frac{2}{5} \) of Principal (P)
- Time (T) = 10 years
- We need to find the Rate of Interest (R).

2. **Use the Simple Interest Formula:**
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]

3. **Substitute the Known Values:**
We know that \( SI = \frac{2}{5}P \) and \( T = 10 \). Substituting these values into the formula gives:
\[ \frac{2}{5}P = \frac{P \times R \times 10}{100} \]

4. **Simplify the Equation:**
First, we can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ \frac{2}{5} = \frac{R \times 10}{100} \]

5. **Cross-Multiply to Solve for R:**
Rearranging the equation gives:
\[ 2 \times 100 = 5 \times R \times 10 \]
\[ 200 = 50R \]

6. **Divide to Find R:**
Now, divide both sides by 50:
\[ R = \frac{200}{50} = 4 \]

7. **Convert to Percentage:**
Since R is already in percentage form, we conclude that:
\[ R = 4\% \]

### Final Answer:
The rate of interest per annum is **4%**.