A,B and C together start a business with a total investment of Rs. 15,000 At the end of the year, the total profit Rs. 3000. What is A's share of profit ?
(i) A's contribution is `(3)/(2)` times that of B.
(ii) B's contribution is twice that of C.
(iii) A's contribution is thrice that of C.

Options

A. (i) and (ii) only
B. (ii) and (iii) only
C. All (i), (ii), and (iii)
D. Any two of the three

Answer

To determine A's share of the profit, we need to analyze the contributions of A, B, and C based on the information provided.

### Step 1: Define the Variables
Let:
- C's contribution = x
- B's contribution = 2x (since B's contribution is twice that of C)
- A's contribution = (3/2) * (2x) = 3x (since A's contribution is (3/2) times that of B)

### Step 2: Set Up the Equation for Total Investment
The total investment by A, B, and C is given as Rs. 15,000. Therefore, we can write the equation:
\[ A + B + C = 15,000 \]
Substituting the contributions:
\[ 3x + 2x + x = 15,000 \]
This simplifies to:
\[ 6x = 15,000 \]

### Step 3: Solve for x
To find the value of x, divide both sides by 6:
\[ x = \frac{15,000}{6} = 2,500 \]

### Step 4: Calculate Individual Contributions
Now we can calculate the contributions of A, B, and C:
- C's contribution = x = Rs. 2,500
- B's contribution = 2x = Rs. 5,000
- A's contribution = 3x = Rs. 7,500

### Step 5: Calculate A's Share of Profit
The total profit is Rs. 3,000. The profit is distributed in the ratio of their contributions. The total contribution is:
\[ A + B + C = 15,000 \]
The ratio of A's contribution to the total contribution is:
\[ \text{A's share of profit} = \left(\frac{A's \ contribution}{Total \ contribution}\right) \times Total \ profit \]
\[ = \left(\frac{7,500}{15,000}\right) \times 3,000 \]
\[ = \frac{1}{2} \times 3,000 = 1,500 \]

### Conclusion
A's share of the profit is Rs. 1,500.

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