A, B and C enter into partnership with capital contribution of 25,000, 30,000 and 15,000 respectively. A is the working partner and he gets 30% of the profit for managing the business. The balance profit is distributed in proportion to the capital investment. At the year-end. A gets Rs. 200 more than B and C together.Find the total profit.

Options

A. 2500
B. 2000
C. 2200
D. 2400

Answer

To solve the problem step by step, let's break it down:

### Step 1: Identify the capital contributions
A, B, and C have the following capital contributions:
- A = Rs. 25,000
- B = Rs. 30,000
- C = Rs. 15,000

### Step 2: Calculate the ratio of their investments
To find the ratio of their investments, we can simplify the contributions:
- A : B : C = 25000 : 30000 : 15000
- Dividing each by 5000 gives us: A : B : C = 5 : 6 : 3

### Step 3: Determine the profit-sharing arrangement
A receives 30% of the total profit for managing the business. The remaining profit (70%) is distributed in the ratio of their investments (5:6:3).

### Step 4: Let the total profit be represented as 'P'
Let the total profit be P. Then:
- A's share from managing the business = 30% of P = 0.3P
- Remaining profit = 70% of P = 0.7P

### Step 5: Distribute the remaining profit
The remaining profit (0.7P) is distributed in the ratio of 5:6:3.
- Total parts = 5 + 6 + 3 = 14 parts
- Value of each part = 0.7P / 14

Now, we can calculate the shares:
- A's share from remaining profit = (5/14) * 0.7P
- B's share from remaining profit = (6/14) * 0.7P
- C's share from remaining profit = (3/14) * 0.7P

### Step 6: Calculate total shares for A, B, and C
- A's total share = 0.3P + (5/14) * 0.7P
- B's total share = (6/14) * 0.7P
- C's total share = (3/14) * 0.7P

### Step 7: Simplify the expressions
Calculating A's total share:
- A's total share = 0.3P + (5/14) * 0.7P
- A's total share = 0.3P + (5 * 0.7P) / 14
- A's total share = 0.3P + (3.5P) / 14
- A's total share = 0.3P + 0.25P = 0.55P

Calculating B's total share:
- B's total share = (6/14) * 0.7P = (3/7) * 0.7P = 0.3P

Calculating C's total share:
- C's total share = (3/14) * 0.7P = (3 * 0.7P) / 14 = 0.15P

### Step 8: Set up the equation based on the problem statement
According to the problem, A gets Rs. 200 more than B and C together:
- A's share = B's share + C's share + 200
- 0.55P = (0.3P + 0.15P) + 200
- 0.55P = 0.45P + 200

### Step 9: Solve for P
- 0.55P - 0.45P = 200
- 0.10P = 200
- P = 2000

### Conclusion
The total profit is Rs. 2000.

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