S, T and U started a business by investing Rs. 4200, Rs. 6300 and Rs. 8400 respectively. S left the business after 3 months, T left 6 months after the business had started and U remained in the business till one year. At the end of one year the total profit is Rs. 6000. What is the U's share (in Rs.) in the profit?

Options

A. 4200
B. 3200
C. 4000
D. 3600

Answer

To solve the problem, we will calculate the effective capital contribution of each partner based on their investment and the duration for which they invested in the business. This will help us determine U's share in the total profit.

### Step-by-Step Solution:

1. **Identify the investments and durations:**
- S's investment = Rs. 4200 for 3 months
- T's investment = Rs. 6300 for 6 months
- U's investment = Rs. 8400 for 12 months

2. **Calculate the effective capital contribution for each partner:**
- For S:
\[ \text{Effective contribution of S} = \text{Investment} \times \text{Time} = 4200 \times 3 = 12600 \]
- For T:
\[ \text{Effective contribution of T} = 6300 \times 6 = 37800 \]
- For U:
\[ \text{Effective contribution of U} = 8400 \times 12 = 100800 \]

3. **Sum of effective contributions:**
\[ \text{Total effective contribution} = 12600 + 37800 + 100800 = 126200 \]

4. **Calculate U's share in the profit:**
- Total profit = Rs. 6000
- U's share of profit is proportional to his effective contribution:
\[ \text{U's share} = \left(\frac{\text{U's effective contribution}}{\text{Total effective contribution}}\right) \times \text{Total profit} \]
\[ \text{U's share} = \left(\frac{100800}{126200}\right) \times 6000 \]

5. **Calculate U's share:**
\[ \text{U's share} = \left(\frac{100800}{126200}\right) \times 6000 \approx 4800 \]

### Final Answer:
U's share in the profit is Rs. 4800.

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