Mr. Dutta desired to deposit his retirement benefit of `Rs.3` lacs partly to a post office and partly to a bank at `10%` and `6%` interests respectively. If his monthly interest income was `Rs. 2000`, then the difference of his deposits in the post office and in the bank was:

Options

A. `Rs. 50,000 `
B. `RS. 40,000`
C. Nil
D. `Rs.1,00,000 `

Answer

To solve the problem, we need to find the difference between Mr. Dutta's deposits in the post office and the bank based on the given interest rates and total monthly interest income.

### Step-by-Step Solution:

1. **Understand the Total Deposit**:
Mr. Dutta has a total retirement benefit of Rs. 3,00,000 (or 3 lacs).

2. **Define Variables**:
Let:
- \( P \) = amount deposited in the post office at 10% interest
- \( B \) = amount deposited in the bank at 6% interest

We know that:
\[ P + B = 3,00,000 \]

3. **Calculate Monthly Interest Income**:
The total monthly interest income is Rs. 2000. Therefore, the annual interest income is:
\[ \text{Annual Interest} = 2000 \times 12 = 24,000 \]

4. **Set Up the Interest Equation**:
The interest earned from both deposits can be expressed as:
\[ \text{Interest from Post Office} + \text{Interest from Bank} = 24,000 \]
This can be calculated as:
\[ 0.10P + 0.06B = 24,000 \]

5. **Substitute for B**:
From the first equation \( P + B = 3,00,000 \), we can express \( B \) in terms of \( P \):
\[ B = 3,00,000 - P \]

6. **Substitute B into the Interest Equation**:
Now substitute \( B \) into the interest equation:
\[ 0.10P + 0.06(3,00,000 - P) = 24,000 \]

7. **Simplify the Equation**:
Expanding the equation:
\[ 0.10P + 18,000 - 0.06P = 24,000 \]
Combine like terms:
\[ 0.04P + 18,000 = 24,000 \]

8. **Isolate P**:
Subtract 18,000 from both sides:
\[ 0.04P = 6,000 \]
Now divide by 0.04:
\[ P = \frac{6,000}{0.04} = 1,50,000 \]

9. **Find B**:
Substitute \( P \) back to find \( B \):
\[ B = 3,00,000 - 1,50,000 = 1,50,000 \]

10. **Calculate the Difference**:
The difference between the deposits in the post office and the bank is:
\[ |P - B| = |1,50,000 - 1,50,000| = 0 \]

### Final Answer:
The difference of his deposits in the post office and in the bank is **Rs. 0**.

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