The simple interset on a sum is `(5)/(9)` th of the principal for 25 years. What is the rate (in per cent) of interset per annum ?

Options

A. `(25)/(9)`
B. `(9)/(2)`
C. `(20)/(9)`
D. `(15)/(4)`

Answer

To find the rate of interest per annum when the simple interest is \( \frac{5}{9} \) of the principal for 25 years, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Simple Interest (SI), Principal (P), Rate (R), and Time (T)**:
The formula for Simple Interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]

2. **Identify the given values**:
- Simple Interest (SI) = \( \frac{5}{9} P \)
- Time (T) = 25 years

3. **Substitute the values into the Simple Interest formula**:
\[ \frac{5}{9} P = \frac{P \times R \times 25}{100} \]

4. **Cancel out the Principal (P)**:
Since P is common on both sides (assuming \( P \neq 0 \)), we can divide both sides by P:
\[ \frac{5}{9} = \frac{R \times 25}{100} \]

5. **Rearranging the equation to solve for R**:
Multiply both sides by 100 to eliminate the fraction:
\[ 100 \times \frac{5}{9} = R \times 25 \]
\[ \frac{500}{9} = R \times 25 \]

6. **Isolate R**:
Divide both sides by 25:
\[ R = \frac{500}{9 \times 25} \]
\[ R = \frac{500}{225} \]
\[ R = \frac{20}{9} \]

7. **Convert R to percentage**:
Since R is already in percentage form, we conclude:
\[ R = \frac{20}{9} \text{ percent} \]

### Final Answer:
The rate of interest per annum is \( \frac{20}{9} \) percent.