X, Y, Z enter into a partnership venture with a capital of Rs.1.20.000, in which the contribution of Y and Z are, respectively, 40% more and Rs.1.000 more than that of X. The profit earned is 20% of the capital. Out of this profit, 10% goes towards some incidental expenses. What is the share (in 3) of X out of it?

Options

A. 7500
B. 4800
C. 7000
D. 6300

Answer

To solve the problem step-by-step, we can follow these calculations:

### Step 1: Define the Contributions
Let the investment of X be \( P \).
- The investment of Y is 40% more than X, which can be expressed as:
\[ Y = P + 0.4P = 1.4P \]
- The investment of Z is Rs. 1000 more than X:
\[ Z = P + 1000 \]

### Step 2: Set Up the Total Investment Equation
The total capital invested by X, Y, and Z is Rs. 120,000. Therefore, we can write:
\[ P + 1.4P + (P + 1000) = 120000 \]
Combining the terms gives:
\[ 3.4P + 1000 = 120000 \]

### Step 3: Solve for P
Subtract 1000 from both sides:
\[ 3.4P = 120000 - 1000 \]
\[ 3.4P = 119000 \]
Now, divide both sides by 3.4 to find \( P \):
\[ P = \frac{119000}{3.4} = 35000 \]

### Step 4: Calculate Individual Contributions
Now we can calculate the contributions of X, Y, and Z:
- Contribution of X:
\[ X = P = 35000 \]
- Contribution of Y:
\[ Y = 1.4P = 1.4 \times 35000 = 49000 \]
- Contribution of Z:
\[ Z = P + 1000 = 35000 + 1000 = 36000 \]

### Step 5: Calculate Total Profit
The total profit earned is 20% of the total capital:
\[ \text{Total Profit} = 0.2 \times 120000 = 24000 \]

### Step 6: Calculate Incidental Expenses
10% of the profit goes towards incidental expenses:
\[ \text{Incidental Expenses} = 0.1 \times 24000 = 2400 \]

### Step 7: Calculate Remaining Profit
Remaining profit after expenses:
\[ \text{Remaining Profit} = 24000 - 2400 = 21600 \]

### Step 8: Calculate Profit Share Ratio
The profit is distributed in the ratio of their investments:
- Total investment = \( 35000 + 49000 + 36000 = 120000 \)
- The ratio of their investments is:
\[ X:Y:Z = 35000:49000:36000 \]

To simplify this ratio:
- Convert to a common scale:
\[ \text{Ratio} = \frac{35000}{35000}:\frac{49000}{35000}:\frac{36000}{35000} = 1:1.4:1.02857 \]
- Multiply through by 100000 to avoid decimals:
\[ 100000:140000:102857 \approx 35:49:36 \]

### Step 9: Calculate X's Share of the Profit
The total parts in the ratio are:
\[ 35 + 49 + 36 = 120 \]
Each part of the profit is:
\[ \text{Value of one part} = \frac{21600}{120} = 180 \]
Thus, X's share of the profit is:
\[ \text{X's Share} = 35 \times 180 = 6300 \]

### Final Answer
The share of X out of the profit is Rs. 6300.

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