A, B and C are partners sharing profits and losses

4 :- A, B, and C are partners sharing profits and losses in the ratio of 5 : 4 : 1. Calculate the new profit sharing ratio, sacrificing ratio, and gaining ratio in each of the following cases:
Case 1. As per new agreement, C acquires 1/5th share from A.
Case 2. As per new agreement, C acquires 1/5th share equally from A and B.
Case 3. As per new agreement, A, B, and C will share future profits and losses equally.
Case 4. As per new agreement, C acquires 1/10th share of A and 1/2 share of B.

Solution:-

CASE 1:- Old ratio of A, B and C = 5:4:1
A’s new share = 5/10 – 1/5 = 3/10
B’s new share = 4/10 – 0 = 4/10
C’s new share = 1/10 + 1/5 = 3/10
Thus, their new proifit sharing ratio is 3:4:3

CASE 2:- Old ratio of A,B and C = 5:4:1
C acquires 1/5 equally from A and B
C acquires from A = 1/5 x 1/2 = 1/10
C acquires from B = 1/5 x 1/2 = 1/10

A’s new share = 5/10 – 1/10 = 4/10
B’s new share = 4/10 – 1/10 = 3/10
C’s new share = 1/10 + 1/5 = 3/10
New profit sharing ratio is 4:3:3
Sacrificing ratio of A and B is 1:1

CASE 3:- Old profit sharing ratio is 5:4:1
New profit sharing ratio is 1:1:1
A = 5/10 – 1/3 = 5/30 (sacrifice)
B = 4/10 – 1/3 = 2/30 (sacrifice)
C = 1/10 – 1/3 = -7/30 (gain)
Sacrificing ratio of A and B is 5:2

CASE 4:- Old ratio of A, B and C is 5:4:1
A’s sacrifice = 5/10 x 1/10 = 5/100
B’s sacrifice = 4/10 x 1/2 = 4/20

A’s new share = 5/10 – 5/100 = 45/100
B’s new share = 4/10 – 4/20 = 4/20 x 5/5 = 20/100
C’s new share = 1/10 + 5/100 + 4/20 = 35/100
New profit sharing ratio =  45:20:35 = 9:4:7
Sacrificing ratio of A and B is 5:20 = 1:4