Mr Dhani Ram lends Rs.1500 to Mr Garib Dass and a certain sum to Mr Majhdaar at the same time at `8%` per annum simple interest. If after 4 years, Dhani Ram altogether receives Rs.1400 as interest from Mr Dass and Mr Majhdaar, then the sum lent to Mr Majhdaar is

Options

A. Rs.2875
B. Rs.1885
C. Rs.2245
D. Rs.2615

Answer

To solve the problem step by step, we will use the formula for simple interest and set up the equations based on the information given.

### Step-by-Step Solution

1. **Identify the Given Information:**
- Amount lent to Mr. Garib Dass = Rs. 1500
- Rate of interest = 8% per annum
- Time period = 4 years
- Total interest received from both Mr. Garib Dass and Mr. Majhdaar = Rs. 1400

2. **Let the Amount Lent to Mr. Majhdaar be x:**
- Therefore, the total principal amount lent = Rs. 1500 + x

3. **Use the Simple Interest Formula:**
- The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
- Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest
- \( T \) = Time in years

4. **Calculate the Interest from Mr. Garib Dass:**
- The interest from Mr. Garib Dass after 4 years can be calculated as:
\[ SI_{Dass} = \frac{1500 \times 8 \times 4}{100} = \frac{48000}{100} = Rs. 480 \]

5. **Calculate the Interest from Mr. Majhdaar:**
- Let the interest from Mr. Majhdaar be \( SI_{Majhdaar} \).
- According to the problem, the total interest received is Rs. 1400:
\[ SI_{Dass} + SI_{Majhdaar} = 1400 \]
- Substituting the value of \( SI_{Dass} \):
\[ 480 + SI_{Majhdaar} = 1400 \]
- Therefore,
\[ SI_{Majhdaar} = 1400 - 480 = Rs. 920 \]

6. **Set Up the Equation for Mr. Majhdaar's Interest:**
- Using the simple interest formula for Mr. Majhdaar:
\[ SI_{Majhdaar} = \frac{x \times 8 \times 4}{100} \]
- Substituting the value of \( SI_{Majhdaar} \):
\[ 920 = \frac{x \times 32}{100} \]

7. **Solve for x:**
- Rearranging the equation:
\[ 920 \times 100 = 32x \]
\[ 92000 = 32x \]
\[ x = \frac{92000}{32} = 2875 \]

8. **Conclusion:**
- The sum lent to Mr. Majhdaar is Rs. 2875.

### Final Answer:
The sum lent to Mr. Majhdaar is Rs. 2875.