A starts a business with Rs 2,000 , B joins him after 3 months with Rs 3,000 . C puts a sum of Rs 9,000 in the business for 2 months each . At the end of the year the business gave a profit of Rs 4600. How should the profit be divided among them ?

Options

A. 1600,1800,1200
B. 1400,1200,2000
C. 1600,1400,1600
D. 1300,1600,1700

Answer

To solve the problem of how to divide the profit among A, B, and C, we need to calculate the effective capital contribution of each partner based on the time they invested in the business. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the effective capital contribution of each partner

1. **A's Contribution:**
- A invests Rs 2,000 for 12 months.
- Effective contribution = 2000 * 12 = Rs 24,000.

2. **B's Contribution:**
- B joins after 3 months, so he invests for 9 months.
- B invests Rs 3,000.
- Effective contribution = 3000 * 9 = Rs 27,000.

3. **C's Contribution:**
- C invests Rs 9,000 for 2 months.
- Effective contribution = 9000 * 2 = Rs 18,000.

### Step 2: Calculate the total effective capital contribution

Now, we sum up the effective contributions of all partners:
- Total effective contribution = A's contribution + B's contribution + C's contribution
- Total effective contribution = 24,000 + 27,000 + 18,000 = Rs 69,000.

### Step 3: Calculate the profit-sharing ratio

Next, we find the ratio of their effective contributions:
- A's share = 24,000
- B's share = 27,000
- C's share = 18,000

To simplify the ratio:
- A : B : C = 24,000 : 27,000 : 18,000
- Dividing each term by 3, we get:
- A : B : C = 8 : 9 : 6

### Step 4: Calculate the total parts in the ratio

Now, we find the total parts in the ratio:
- Total parts = 8 + 9 + 6 = 23 parts.

### Step 5: Calculate the value of each part

Given that the total profit is Rs 4,600:
- Value of 1 part = Total Profit / Total parts = 4600 / 23 = Rs 200.

### Step 6: Calculate each partner's share of the profit

Now we can calculate the profit share for each partner:
1. **A's share:**
- A's share = 8 parts = 8 * 200 = Rs 1,600.

2. **B's share:**
- B's share = 9 parts = 9 * 200 = Rs 1,800.

3. **C's share:**
- C's share = 6 parts = 6 * 200 = Rs 1,200.

### Final Result

Thus, the profit should be divided as follows:
- A: Rs 1,600
- B: Rs 1,800
- C: Rs 1,200

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