If the difference between the simple interest on a certain sum of money for 4 years at 2%% per annum and the simple interest on the same sum for the same period at 3% per annum is 60, then find the sum.

Options

A. Rs 3,000
B. Rs 3,500
C. Rs 2,500
D. Rs 2,000

Answer

To solve the problem step-by-step, we will use the formula for Simple Interest (SI):

\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (the sum of money)
- \( R \) = Rate of interest (in percentage)
- \( T \) = Time (in years)

### Step 1: Define the variables
Let \( P \) be the principal amount.

### Step 2: Calculate Simple Interest for both rates
1. **For 2% per annum:**
\[ \text{SI}_1 = \frac{P \times 2 \times 4}{100} = \frac{8P}{100} = \frac{2P}{25} \]

2. **For 3% per annum:**
\[ \text{SI}_2 = \frac{P \times 3 \times 4}{100} = \frac{12P}{100} = \frac{3P}{25} \]

### Step 3: Find the difference in Simple Interest
According to the problem, the difference between the two Simple Interests is given as 60:
\[ \text{SI}_2 - \text{SI}_1 = 60 \]
Substituting the values we calculated:
\[ \frac{3P}{25} - \frac{2P}{25} = 60 \]

### Step 4: Simplify the equation
\[ \frac{3P - 2P}{25} = 60 \]
\[ \frac{P}{25} = 60 \]

### Step 5: Solve for \( P \)
To find \( P \), multiply both sides by 25:
\[ P = 60 \times 25 \]
\[ P = 1500 \]

### Step 6: Conclusion
The sum (the principal amount) is \( 1500 \).

---