A and B are two partners sharing profit and losses on the ratio of 3:2...
Given, A:B=3:2
Or 3/5, 2/5
C is admitted 1/5 th share
acquire equally from A and B
From A=1/5 *1/2=1/10
B=1/5 *1/2=1/10
Therefore, x=3/5 - 1/10 =5/10
Y=2/5 -1/10 =3/10
Z=1/5 * 2/2=2/10
So, new profit sharing ratio of A:B:C is 5:3:2
And, we know that sacrificing ratio = old ratio- new ratio
A's sacrifice =3/5 -5/10=1/10
B's sacrifice =2/5 -3/10 =1/10
A and B are two partners sharing profit and losses on the ratio of 3:2...
Profit Sharing Ratio:
Initially, A and B are sharing profit and losses in the ratio of 3:2. This means that out of the total profit, A gets 3 parts and B gets 2 parts. Let's assume that the total profit is P.
- A's share of profit = 3/5 * P
- B's share of profit = 2/5 * P
New Partner C:
C is admitted as a new partner and acquires 1/5 share of the future profit. We know that C has acquired this share equally from A and B. Let's assume that C's share of the profit is x.
- C's share of the profit from A = x/2
- C's share of the profit from B = x/2
Therefore, the total profit share of C is (x/2) + (x/2) = x.
New Profit Sharing Ratio:
Now, let's calculate the new profit sharing ratio including C.
- A's new share of profit = 3/5 * P - x/2
- B's new share of profit = 2/5 * P - x/2
- C's share of profit = x
The new profit sharing ratio can be calculated as follows:
- A's share : B's share : C's share
- (3/5 * P - x/2) : (2/5 * P - x/2) : x
Sacrificing Ratio:
The sacrificing ratio is the ratio in which the existing partners (A and B) give up their share of profit to accommodate the new partner (C). In this case, both A and B give up an equal share to C.
The sacrificing ratio can be calculated as follows:
- Sacrificing ratio = x/2 : x/2
- Simplifying, we get 1 : 1
Therefore, the sacrificing ratio is 1:1, which means that A and B sacrifice their equal shares of profit to accommodate C.
Summary:
The new profit sharing ratio after admitting partner C is (3/5 * P - x/2) : (2/5 * P - x/2) : x. The sacrificing ratio is 1:1, implying that A and B sacrifice their equal shares to accommodate C.