A,B and C enter into partnership . A invests some money at the beginning .B invests double the amount after 6 months and C invests thrice the amount after 8 months . If the annual profit be Rs 18000 C's share is

Options

A. Rs 7500
B. Rs 7200
C. Rs 6000
D. Rs 5750

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Investments
Let the amount invested by A be \( X \).
Then, the amount invested by B is \( 2X \) (since B invests double the amount of A).
The amount invested by C is \( 3X \) (since C invests thrice the amount of A).

### Step 2: Determine the Time of Investment
- A invests for the entire year, which is 12 months.
- B invests for 6 months (since he invests after 6 months).
- C invests for 4 months (since he invests after 8 months).

### Step 3: Calculate the Capital Contribution
The capital contribution of each partner can be calculated by multiplying the amount invested by the time (in months) for which it was invested.

- A's contribution = \( X \times 12 = 12X \)
- B's contribution = \( 2X \times 6 = 12X \)
- C's contribution = \( 3X \times 4 = 12X \)

### Step 4: Find the Total Contribution
Now, we can find the total contribution:
\[ \text{Total Contribution} = A's Contribution + B's Contribution + C's Contribution = 12X + 12X + 12X = 36X \]

### Step 5: Determine the Profit Sharing Ratio
The profit sharing ratio is based on their contributions:
- A's share = \( 12X \)
- B's share = \( 12X \)
- C's share = \( 12X \)

Thus, the ratio of their shares is:
\[ A : B : C = 12X : 12X : 12X = 1 : 1 : 1 \]

### Step 6: Calculate C's Share of the Profit
The total annual profit is Rs 18,000. Since the profit is shared equally among A, B, and C:
\[ C's \text{ share} = \frac{1}{3} \times 18000 = 6000 \]

### Final Answer
C's share of the profit is Rs 6000.

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