To determine the new profit-sharing ratio and sacrificing ratio after admitting partner C, we need to first understand the current structure of profit-sharing between A and B.
Currently, A and B share profits in the ratio of 3:2. This implies:
- A’s share = 3/5
- B’s share = 2/5
With the new partner C joining for a 1/4th share, we must calculate the remaining share that A and B will have after allocating C’s share.
The total profit-sharing ratio must always sum to 1 (or 100%). So, if C takes 1/4, the combined share for A and B will be:
Remaining share for A and B = 1 – 1/4 = 3/4
Now, we need to maintain the existing ratio of A and B. To do this, we’ll calculate their new shares from the 3/4 share that they will keep:
- A’s new share = (3/5) * (3/4) = 9/20
- B’s new share = (2/5) * (3/4) = 6/20
Thus, the new profit sharing will be:
- A’s new share = 9/20
- B’s new share = 6/20
- C’s share = 1/4 = 5/20
Now, let’s determine the sacrificing ratio. This ratio reflects how much A and B sacrifice from their original shares to accommodate C. First, we see their old shares:
- A’s old share = 3/5 = 12/20
- B’s old share = 2/5 = 8/20
Now we can calculate the amount sacrificed by both A and B:
- A’s sacrifice = Old share – New share = 12/20 – 9/20 = 3/20
- B’s sacrifice = Old share – New share = 8/20 – 6/20 = 2/20
Thus, the sacrificing ratio of A to B is:
3/20 : 2/20 or simply 3:2
In conclusion, the new profit-sharing ratio will be 9:6:5 (A:B:C) and the sacrificing ratio will be 3:2 (A:B).