X,Y,Z enter into partnership with capital contribution Rs 50000, 20000 and 30000 respectively .X is a working partner and get 20 % of profit for managing the business .The remaining profit is distributed in the respect of capital . If the end of a year ,X gets Rs 300 more than Y and Z together ,then find total profit is ?

Options

A. A)Rs 1200
B. B)Rs 1700
C. C)Rs 2200
D. D)Rs 1500

Answer

To solve the problem step by step, we need to analyze the partnership contributions and how the profits are distributed.

### Step 1: Determine the Capital Contributions
X, Y, and Z have contributed the following amounts:
- X: Rs 50,000
- Y: Rs 20,000
- Z: Rs 30,000

### Step 2: Calculate the Ratio of Capital Contributions
To find the ratio of their investments, we can express their contributions in a simplified form:
- The ratio of X:Y:Z = 50000:20000:30000 = 5:2:3

### Step 3: Determine the Total Capital Ratio
Since all partners invested for the same time period (1 year), the ratio remains:
- X:Y:Z = 5:2:3

### Step 4: Calculate Total Parts in the Profit Sharing
The total parts in the profit sharing based on their capital contributions is:
- Total parts = 5 + 2 + 3 = 10 parts

### Step 5: Calculate X's Share of Profit for Managing the Business
X receives 20% of the total profit for managing the business. Let the total profit be P.
- X's management share = 20% of P = 0.2P

### Step 6: Calculate Remaining Profit to be Distributed
The remaining profit after X's management share is:
- Remaining profit = P - 0.2P = 0.8P

### Step 7: Distribute Remaining Profit According to Capital Ratio
The remaining profit (0.8P) is distributed in the ratio of their capital contributions (5:2:3).
- X's share from remaining profit = (5/10) * 0.8P = 0.4P
- Y's share from remaining profit = (2/10) * 0.8P = 0.16P
- Z's share from remaining profit = (3/10) * 0.8P = 0.24P

### Step 8: Calculate Total Profit Received by X
Total profit received by X is:
- Total profit for X = X's management share + X's share from remaining profit
- Total profit for X = 0.2P + 0.4P = 0.6P

### Step 9: Calculate Total Profit Received by Y and Z
Total profit received by Y and Z together:
- Total profit for Y + Z = Y's share + Z's share
- Total profit for Y + Z = 0.16P + 0.24P = 0.4P

### Step 10: Set Up the Equation Based on Given Information
According to the problem, X receives Rs 300 more than Y and Z together:
- 0.6P = 0.4P + 300

### Step 11: Solve for Total Profit P
Now, we solve the equation:
- 0.6P - 0.4P = 300
- 0.2P = 300
- P = 300 / 0.2
- P = 1500

### Conclusion
The total profit at the end of the year is Rs 1500.

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