C and D started a business by investing Rs 4000 and Rs 5000 respectively. After 3 months, C withdraws Rs 1000 while D invest Rs 1000 more after 6 months of the starting of business. At the end of the year C’s share is Rs 3900. What will be the total profit (in Rs) at the end of year?

Options

A. 7800
B. 10500
C. 8400
D. 12200

Answer

To solve the problem, we need to calculate the total profit made by C and D at the end of the year based on their investments and the time for which they invested.

### Step-by-Step Solution:

1. **Initial Investments**:
- C invests Rs 4000.
- D invests Rs 5000.

2. **Calculate Capital Contribution**:
- C's investment for the first 3 months: Rs 4000.
- D's investment for the first 6 months: Rs 5000.

3. **Changes After 3 Months**:
- After 3 months, C withdraws Rs 1000, so C's new investment becomes Rs 3000.
- D continues with Rs 5000 for the first 6 months and then adds Rs 1000, making it Rs 6000 after 6 months.

4. **Calculate Time Periods**:
- C's investment:
- Rs 4000 for the first 3 months = 4000 * 3 = 12000 (capital-months)
- Rs 3000 for the next 9 months = 3000 * 9 = 27000 (capital-months)
- Total for C = 12000 + 27000 = 39000 capital-months.

- D's investment:
- Rs 5000 for the first 6 months = 5000 * 6 = 30000 (capital-months)
- Rs 6000 for the next 6 months = 6000 * 6 = 36000 (capital-months)
- Total for D = 30000 + 36000 = 66000 capital-months.

5. **Total Capital Contribution**:
- Total capital-months = C's capital-months + D's capital-months = 39000 + 66000 = 105000 capital-months.

6. **Profit Sharing Ratio**:
- C's share of profit = C's capital-months / Total capital-months = 39000 / 105000 = 39/105 = 13/35.
- D's share of profit = D's capital-months / Total capital-months = 66000 / 105000 = 66/105 = 22/35.

7. **C’s Share of Profit**:
- According to the problem, C's share at the end of the year is Rs 3900.
- Let the total profit be P.
- C's share = (13/35) * P = 3900.
- Thus, P = 3900 * (35/13) = 10500.

8. **Total Profit**:
- Therefore, the total profit at the end of the year is Rs 10500.

### Final Answer:
The total profit at the end of the year is **Rs 10500**.