The rate of simple interest at which a sum of money becomes three times in 25 years is :

Options

A. 6%
B. 8%
C. 5%
D. 4%

Answer

To find the rate of simple interest at which a sum of money becomes three times in 25 years, we can follow these steps:

### Step 1: Define the Variables
Let the principal amount be \( P \). According to the problem, the amount becomes three times the principal in 25 years. Therefore, the amount \( A \) can be expressed as:
\[ A = 3P \]

### Step 2: Write the Formula for Simple Interest
The formula for the amount in simple interest is given by:
\[ A = P + SI \]
where \( SI \) is the simple interest. The simple interest can also be calculated using the formula:
\[ SI = \frac{P \times R \times T}{100} \]
where \( R \) is the rate of interest per annum and \( T \) is the time in years.

### Step 3: Substitute the Known Values
Substituting the known values into the amount formula:
\[ 3P = P + \frac{P \times R \times 25}{100} \]

### Step 4: Rearrange the Equation
Now, rearranging the equation to isolate the simple interest term:
\[ 3P - P = \frac{P \times R \times 25}{100} \]
This simplifies to:
\[ 2P = \frac{P \times R \times 25}{100} \]

### Step 5: Cancel the Principal
Since \( P \) is common on both sides and \( P \neq 0 \), we can cancel \( P \):
\[ 2 = \frac{R \times 25}{100} \]

### Step 6: Solve for the Rate \( R \)
Now, we can solve for \( R \) by multiplying both sides by 100:
\[ 200 = R \times 25 \]
Next, divide both sides by 25:
\[ R = \frac{200}{25} = 8 \]

### Step 7: Conclusion
Thus, the rate of simple interest at which the sum of money becomes three times in 25 years is:
\[ \boxed{8\%} \]