Simple interest on a certain sum for 6 years is `(9)/(25)` of the sum . The rate of interest is

Options

A. 0.06
B. `6(1)/(2)%`
C. `8%`
D. `8(1)/(2)%`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
We know that the simple interest (SI) for 6 years is \( \frac{9}{25} \) of the principal (P).

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 3: Set up the equation
From the problem, we can express the Simple Interest in terms of the principal:
\[ SI = \frac{9}{25} P \]
Now, substituting this into the formula for Simple Interest, we get:
\[ \frac{9}{25} P = \frac{P \times R \times 6}{100} \]

### Step 4: Simplify the equation
We can divide both sides by \( P \) (assuming \( P \neq 0 \)):
\[ \frac{9}{25} = \frac{R \times 6}{100} \]

### Step 5: Cross-multiply to solve for R
Cross-multiplying gives us:
\[ 9 \times 100 = 25 \times R \times 6 \]
This simplifies to:
\[ 900 = 150R \]

### Step 6: Solve for R
Now, divide both sides by 150:
\[ R = \frac{900}{150} = 6 \]

### Conclusion
The rate of interest \( R \) is 6%.