A and B entered Into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs. 26400 after one year by

Options

A. Rs 2400
B. Rss 1200
C. Rs 3600
D. Rs 4800

Answer

To solve the problem, we need to calculate the effective capital contributions of A, B, and C over the year and then determine the profit share of each partner based on their contributions.

### Step-by-Step Solution:

1. **Calculate A's Contribution:**
- A invests Rs. 16,000 for the first 3 months.
- After 3 months, A withdraws Rs. 5,000, leaving Rs. 11,000 for the next 9 months.
- Total contribution of A:
- For the first 3 months: \( 16,000 \times 3 = 48,000 \)
- For the next 9 months: \( 11,000 \times 9 = 99,000 \)
- Total contribution of A = \( 48,000 + 99,000 = 147,000 \)

2. **Calculate B's Contribution:**
- B invests Rs. 12,000 for the first 3 months.
- After 3 months, B invests an additional Rs. 5,000, making it Rs. 17,000 for the next 9 months.
- Total contribution of B:
- For the first 3 months: \( 12,000 \times 3 = 36,000 \)
- For the next 9 months: \( 17,000 \times 9 = 153,000 \)
- Total contribution of B = \( 36,000 + 153,000 = 189,000 \)

3. **Calculate C's Contribution:**
- C joins after 6 months with a capital of Rs. 21,000.
- C's contribution for the last 6 months:
- \( 21,000 \times 6 = 126,000 \)

4. **Total Contributions:**
- Total contributions of A, B, and C:
- A = 147,000
- B = 189,000
- C = 126,000
- Total = \( 147,000 + 189,000 + 126,000 = 462,000 \)

5. **Calculate Profit Shares:**
- Total profit = Rs. 26,400
- Ratio of contributions:
- A's share = \( \frac{147,000}{462,000} \)
- B's share = \( \frac{189,000}{462,000} \)
- C's share = \( \frac{126,000}{462,000} \)

6. **Calculate Individual Shares of Profit:**
- A's profit = \( \frac{147,000}{462,000} \times 26,400 = 8,400 \)
- B's profit = \( \frac{189,000}{462,000} \times 26,400 = 10,800 \)
- C's profit = \( \frac{126,000}{462,000} \times 26,400 = 7,200 \)

7. **Determine How Much B's Share Exceeds C's Share:**
- Difference = B's profit - C's profit
- Difference = \( 10,800 - 7,200 = 3,600 \)

### Final Answer:
B's share exceeds C's share by Rs. 3,600.