 A, B, and C started a business with investments of $5000, $6000, and $7000 respectively. After 4 months, A withdraws $1000, B withdraws $1200, and C withdraws $1400. If the total profit at the end of the year is $18000, what is B's share of the profit?

To determine B's share of the profit, we will use the concept of proportional profit distribution based on each partner's capital investment and the time their capital remained in the business.

### Step-by-step breakdown:

#### 1. **Initial Investments:**
- A invests $5000.
- B invests $6000.
- C invests $7000.

#### 2. **Withdrawals After 4 Months:**
- After 4 months, A withdraws $1000, B withdraws $1200, and C withdraws $1400.

#### 3. **Investment Time Calculation:**
We need to calculate the effective investment of each partner over the entire year. Since withdrawals happen after 4 months, we divide the year into two periods: 4 months before the withdrawal and 8 months after.

#### 4. **Effective Capital Contribution:**

- **A's investment:**
  - For the first 4 months: $5000.
  - For the remaining 8 months: $5000 - $1000 = $4000.
  - A's effective capital contribution = $ (5000 \times 4) + (4000 \times 8) = 20000 + 32000 = 52000 $.

- **B's investment:**
  - For the first 4 months: $6000.
  - For the remaining 8 months: $6000 - $1200 = $4800.
  - B's effective capital contribution = $ (6000 \times 4) + (4800 \times 8) = 24000 + 38400 = 62400 $.

- **C's investment:**
  - For the first 4 months: $7000.
  - For the remaining 8 months: $7000 - $1400 = $5600.
  - C's effective capital contribution = $ (7000 \times 4) + (5600 \times 8) = 28000 + 44800 = 72800 $.

#### 5. **Total Effective Capital:**
The total effective capital of the business is:
\[
52000 \ (\text{A}) + 62400 \ (\text{B}) + 72800 \ (\text{C}) = 187200.
\]

#### 6. **Profit Distribution:**
The profit will be distributed in proportion to their effective capital contributions.

- A's share of the profit = $ \frac{52000}{187200} \times 18000 $.
- B's share of the profit = $ \frac{62400}{187200} \times 18000 $.
- C's share of the profit = $ \frac{72800}{187200} \times 18000 $.

Let's calculate B's share:

\[
B's\ share = \frac{62400}{187200} \times 18000 = \frac{1}{3} \times 18000 = 6000.
\]

### Final Answer:
B's share of the profit is **$6000**.

Would you like further clarification on any of these steps?

#### Related questions:
1. How would A's share of the profit be calculated?
2. How do time and investment influence profit distribution in partnership businesses?
3. What if C had withdrawn more after 4 months? How would it affect the profit shares?
4. How does this method change if more frequent capital withdrawals or investments occur?
5. What happens if one partner exits the business mid-year in such problems?

**Tip:** Always separate the total period into smaller intervals when investments change, to handle such partnership problems effectively.

A, B, and C started a business with investments of $5000, $6000, and $7000 respectively. After 4 months, A withdraws $1000, B withdraws $1200, and C withdraws $1400. If the total profit at the end of the year is $18000, what is B's share of the profit?

Learn how to calculate B's share of the profit in a business where A, B, and C started with different investments and made withdrawals after 4 months. This detailed solution covers proportional profit distribution based on capital investment and time. Suitable for students in Grades 10-12.

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