A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned ?

Options

A. Rs. 35
B. Rs. 245
C. Rs. 350
D. Cannot be determined

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI) and analyze the situation given in the question.

### Step 1: Understand the formula for Simple Interest
The formula for Simple Interest is given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest (annual)
- \( T \) = Time (in years)

### Step 2: Identify the known values
From the question, we know:
- The Simple Interest earned after 7 years is Rs. 1750.
- The time \( T = 7 \) years.

### Step 3: Set up the equation using the known values
We can substitute the known values into the SI formula:
\[ 1750 = \frac{P \times R \times 7}{100} \]

### Step 4: Rearranging the equation
To find \( P \times R \), we can rearrange the equation:
\[ P \times R = \frac{1750 \times 100}{7} \]
\[ P \times R = \frac{175000}{7} \]
\[ P \times R = 25000 \]

### Step 5: Calculate the new interest with an increased rate
Now, if the interest rate is increased by 2%, the new rate will be \( R + 2 \). The new Simple Interest can be calculated as:
\[ \text{SI}_{\text{new}} = \frac{P \times (R + 2) \times 7}{100} \]

### Step 6: Substitute \( P \times R \) into the new interest formula
We can express \( \text{SI}_{\text{new}} \) as:
\[ \text{SI}_{\text{new}} = \frac{P \times R \times 7}{100} + \frac{P \times 2 \times 7}{100} \]
\[ \text{SI}_{\text{new}} = 1750 + \frac{P \times 14}{100} \]

### Step 7: Find the additional interest earned
The additional interest earned due to the increase in the rate is:
\[ \text{Additional Interest} = \text{SI}_{\text{new}} - \text{SI} \]
\[ \text{Additional Interest} = \frac{P \times 14}{100} \]

### Step 8: Substitute \( P \) to find the additional interest
To find the additional interest, we need to express \( P \) in terms of \( R \):
Since \( P \times R = 25000 \), we can express \( P \) as:
\[ P = \frac{25000}{R} \]

Substituting \( P \) into the additional interest formula:
\[ \text{Additional Interest} = \frac{\left(\frac{25000}{R}\right) \times 14}{100} \]
\[ \text{Additional Interest} = \frac{350000}{R} \]

### Conclusion
The additional interest earned when the rate increases by 2% depends on the value of \( R \). However, without knowing the exact value of \( R \), we cannot determine the exact amount of additional interest.