A started a business with a capital of Rs 112000. After 2 months , B joined the business with a capital of Rs 80000,and after another 2 months, C joined the business with a capital of Rs 72000. After 10 months from the starts of the business, B withdrew Rs 8000 and C also withdrew Rs 8000. if B received Rs 9800 as his share in the profit at the end of a year, then the total profit was `:`

Options

A. Rs 35800
B. Rs 30800
C. Rs 32400
D. Rs 33600

Answer

To solve the problem step by step, we need to calculate the effective capital contribution of each partner (A, B, and C) based on the time they invested in the business.

### Step 1: Calculate the effective capital contribution for each partner.

1. **A's contribution:**
- Capital = Rs 112,000
- Time = 12 months
- Effective capital = 112,000 * 12 = Rs 1,344,000

2. **B's contribution:**
- Capital = Rs 80,000
- Time = 10 months (joined after 2 months)
- Effective capital = 80,000 * 10 = Rs 800,000

3. **C's contribution:**
- Capital = Rs 72,000
- Time = 6 months (joined after 4 months)
- Effective capital = 72,000 * 6 = Rs 432,000

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

Total effective capital = A's effective capital + B's effective capital + C's effective capital

= 1,344,000 + 800,000 + 432,000 = Rs 2,576,000

### Step 3: Calculate the ratio of their effective capital contributions.

The ratio of A : B : C = 1,344,000 : 800,000 : 432,000

To simplify this ratio, we can divide each term by 16,000:

- A's share = 1,344,000 / 16,000 = 84
- B's share = 800,000 / 16,000 = 50
- C's share = 432,000 / 16,000 = 27

Thus, the ratio of A : B : C = 84 : 50 : 27.

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

Total parts = 84 + 50 + 27 = 161 parts.

### Step 5: Find B's share in the profit.

Given that B received Rs 9,800 as his share of the profit, we can find the total profit using the ratio of B's share to the total parts.

B's share = (B's part / Total parts) * Total Profit

So, we have:

9,800 = (50 / 161) * Total Profit

### Step 6: Solve for Total Profit.

Total Profit = 9,800 * (161 / 50)

Calculating this gives:

Total Profit = 9,800 * 3.22 = Rs 31,596.

### Final Answer:

The total profit at the end of the year is Rs 31,596.

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