An amount was invested at a simple rate of interest p.a. for 5 years. It would have fetched Rs.300 more had it been invested at 2% higher rate. What was the amount invested?

Options

A. Rs 3300
B. Rs.3000
C. Rs 2000
D. Rs. 2300

Answer

To solve the problem, we need to use the formula for Simple Interest (SI) and understand the relationship between the principal amount, the rate of interest, and the time period.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that an amount \( P \) is invested at a simple interest rate \( R \% \) for 5 years. If the rate were increased by 2%, the interest earned would be Rs. 300 more.

2. **Formula for Simple Interest**:
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and \( T \) is the time in years.

3. **Calculate Interest at Original Rate**:
The interest earned at the original rate \( R \) for 5 years is:
\[ \text{SI}_1 = \frac{P \times R \times 5}{100} \]

4. **Calculate Interest at Increased Rate**:
The interest earned at the increased rate \( (R + 2) \) for 5 years is:
\[ \text{SI}_2 = \frac{P \times (R + 2) \times 5}{100} \]

5. **Setting Up the Equation**:
According to the problem, the difference between the two interests is Rs. 300:
\[ \text{SI}_2 - \text{SI}_1 = 300 \]
Substituting the expressions for \( \text{SI}_1 \) and \( \text{SI}_2 \):
\[ \frac{P \times (R + 2) \times 5}{100} - \frac{P \times R \times 5}{100} = 300 \]

6. **Simplifying the Equation**:
Factor out common terms:
\[ \frac{5P}{100} \left((R + 2) - R\right) = 300 \]
This simplifies to:
\[ \frac{5P \times 2}{100} = 300 \]

7. **Solving for \( P \)**:
Simplifying further:
\[ \frac{10P}{100} = 300 \]
\[ \frac{P}{10} = 300 \]
\[ P = 3000 \]

### Conclusion:
The amount invested is **Rs. 3000**.