A starts a business with X 4000. B joins him after 3 months with X 8000. C puts a sum of X 20000 in the business for 2 months only. At the end of year, the business gives a profits of X 16800 . How should the profit be divided amongst them ?

Options

A. A = 5040 B = 7560, C = 4200
B. A= 7560, B = 5040,C = 4200
C. A=4200,B= 7560 ,c = 5040
D. A= 4200,B = 040,C=7560

Answer

To solve the problem, we need to calculate the profit-sharing ratio based on the capital invested by A, B, and C and the duration for which they invested their capital.

### Step 1: Calculate the capital contribution of each partner.

- **A's investment**: A invests X 4000 for 12 months.
- **B's investment**: B invests X 8000 but joins after 3 months, so he invests for 9 months.
- **C's investment**: C invests X 20000 for only 2 months.

### Step 2: Calculate the effective capital contribution for each partner.

To find the effective capital contribution, we multiply the amount invested by the number of months it was invested.

- **A's effective capital** = 4000 * 12 = 48000
- **B's effective capital** = 8000 * 9 = 72000
- **C's effective capital** = 20000 * 2 = 40000

### Step 3: Determine the total effective capital contribution.

Now, we add the effective capital contributions of all partners:

Total effective capital = A's effective capital + B's effective capital + C's effective capital
Total effective capital = 48000 + 72000 + 40000 = 160000

### Step 4: Calculate the profit-sharing ratio.

Now, we can find the ratio of their effective capital contributions:

- A's ratio = 48000 / 160000 = 3/10
- B's ratio = 72000 / 160000 = 9/20
- C's ratio = 40000 / 160000 = 1/4

To express these ratios in a simpler form, we can convert them to a common denominator:

- A's share = 48000 : 160000 = 6 : 9 : 5

### Step 5: Calculate each partner's share of the profit.

The total profit is X 16800. We will distribute this profit according to the ratios calculated.

- Total parts = 6 + 9 + 5 = 20

Now, we can find each partner's share:

- **A's share** = (6/20) * 16800 = 5040
- **B's share** = (9/20) * 16800 = 7560
- **C's share** = (5/20) * 16800 = 4200

### Conclusion:

- A's share = X 5040
- B's share = X 7560
- C's share = X 4200