A person borrows Rs 75,000 for 3 years at 5% simple interest. He lends it to B at 7% for 3 years. What is his gain (in Rs)?

Options

A. 3500
B. 4500
C. 6000
D. 5000

Answer

To solve the problem, we need to calculate the gain the person makes by borrowing money at a lower interest rate and lending it at a higher interest rate.

### Step-by-Step Solution:

1. **Identify the Principal Amount**:
The person borrows Rs 75,000.

2. **Identify the Interest Rates**:
- Borrowing rate: 5%
- Lending rate: 7%

3. **Calculate the Interest Paid on Borrowing**:
We will use the formula for Simple Interest (SI):
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (Rs 75,000)
- \( R \) = Rate of interest (5%)
- \( T \) = Time (3 years)

Plugging in the values:
\[ \text{SI}_{\text{borrowed}} = \frac{75000 \times 5 \times 3}{100} = \frac{1125000}{100} = 11250 \]
So, the interest paid on borrowing is Rs 11,250.

4. **Calculate the Interest Earned from Lending**:
Now, we will calculate the interest earned by lending the same amount at 7% for 3 years:
\[ \text{SI}_{\text{lent}} = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount (Rs 75,000)
- \( R \) = Rate of interest (7%)
- \( T \) = Time (3 years)

Plugging in the values:
\[ \text{SI}_{\text{lent}} = \frac{75000 \times 7 \times 3}{100} = \frac{1575000}{100} = 15750 \]
So, the interest earned from lending is Rs 15,750.

5. **Calculate the Gain**:
The gain is the difference between the interest earned and the interest paid:
\[ \text{Gain} = \text{SI}_{\text{lent}} - \text{SI}_{\text{borrowed}} = 15750 - 11250 = 4500 \]

Thus, the person's gain is **Rs 4,500**.

### Final Answer:
The gain is Rs 4,500.