In how many years will a certain sum be thrice of itself at the rate of 5 % per annum simple interest ?

Options

A. 30 years
B. 40 years
C. 25 years
D. 20 years

Answer

To solve the problem of how many years it will take for a certain sum to become thrice itself at a rate of 5% per annum simple interest, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find the time (T) it takes for a principal amount (P) to grow to three times its original amount (3P) at a simple interest rate of 5% per annum.

2. **Setting Up the Formula**:
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- SI = Simple Interest
- P = Principal amount
- R = Rate of interest (5% in this case)
- T = Time in years

3. **Finding the Simple Interest**:
Since the amount becomes three times the principal, we can express this as:
\[ A = P + SI \]
Given that \( A = 3P \), we can find the Simple Interest:
\[ SI = A - P = 3P - P = 2P \]

4. **Substituting into the Formula**:
Now we can substitute SI into the simple interest formula:
\[ 2P = \frac{P \times 5 \times T}{100} \]

5. **Simplifying the Equation**:
We can cancel P from both sides (assuming P ≠ 0):
\[ 2 = \frac{5T}{100} \]

6. **Cross-Multiplying**:
To eliminate the fraction, we can cross-multiply:
\[ 2 \times 100 = 5T \]
\[ 200 = 5T \]

7. **Solving for T**:
Now, divide both sides by 5 to find T:
\[ T = \frac{200}{5} = 40 \]

### Final Answer:
It will take **40 years** for the sum to become thrice itself at a rate of 5% per annum simple interest.

---