A,B and C enter into a partnership.A invests some amount at the beginning , B invests double the amount of A after 6 months and C invests thrice the amount of A after 8 months. If the annual profit be X 54000, find the Cs share

Options

A. X 3000
B. X 18000
C. X 15000
D. X 21000

Answer

To solve the problem step by step, we need to determine the investment and the time for which each partner invested their money. Let's denote the amount invested by A as \( A \).

### Step 1: Determine the investments and time periods for A, B, and C.

- A invests \( A \) at the beginning for 12 months.
- B invests double the amount of A, which is \( 2A \), but he invests it after 6 months. Therefore, B's investment is for \( 12 - 6 = 6 \) months.
- C invests three times the amount of A, which is \( 3A \), but he invests it after 8 months. Therefore, C's investment is for \( 12 - 8 = 4 \) months.

### Step 2: Calculate the capital contribution of each partner.

To find the effective capital contribution, we multiply the amount invested by the time period (in months):

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

### Step 3: Find the total contributions.

Now, we can sum up the contributions:

\[ \text{Total contribution} = 12A + 12A + 12A = 36A \]

### Step 4: Determine the share of each partner in the profit.

The total profit is given as \( 54000 \). The profit share for each partner is proportional to their contribution.

- A's share = \( \frac{12A}{36A} \times 54000 = \frac{1}{3} \times 54000 = 18000 \)
- B's share = \( \frac{12A}{36A} \times 54000 = \frac{1}{3} \times 54000 = 18000 \)
- C's share = \( \frac{12A}{36A} \times 54000 = \frac{1}{3} \times 54000 = 18000 \)

### Step 5: Conclusion

Since all partners have equal contributions in terms of effective capital, they will share the profit equally. Thus, C's share of the profit is:

\[ \text{C's share} = 18000 \]