A, B and C are partners sharing profits and losses in the ratio of 5 : 4 : 1. Calculate new profit-sharing ratio, sacrificing ratio and gaining ratio in each of the following cases: Case 1. C acquires 1/5th share from A. Case 2. C acquires 1/5th share equally form A and B. Case 3. A, B and C will share future profits and losses equally. Case 4. 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 Sacrifice =1/5 to C
C’s Gain = 1/5

Therefore,
A’s New Share = 5/10 -1/5 = 5 – 2/10 = 3/10
B’s Share = 4/10
C’s New Share = 1/10 + 1/5 = 1 + 2/10 = 3/10

Therefore, New Ratio of A, B and C = 3: 4: 3

Case 2:

Old Ratio of A, B and C = 5: 4: 1
A’s Sacrifice = 1/10 to C
B’s Sacrifice = 1/10 to C C’s gain = 1/5

Therefore,
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 = 1+2/10 = 3/10

Therefore, New Ratio of A, B and C = 4: 3: 3

Case 3:

Old Ratio of A, B and C = 5: 4: 1
New Ratio of A, B and C = 1: 1: 1
Sacrificing Ratio = Old Ratio − New Ratio
Gaining Ratio = New Ratio – Old Ratio

Therefore,
A = 5/10 – 1/3 = 15 – 10/30 = 5/30
B = 4/10 – 1/3 = 12 – 10/30 = 2/30
C = 1/10 – 1/3 = 3 – 10/30 = -3/10

Therefore, A’s sacrifice = 5/30, B’s sacrifice = 2/30 and C’s gain = 3/10

Case 4:

Old Ratio of A, B and C = 5:4:1
A’s sacrifice = 5/10 x 1/10 = 1/20 to C
B’s sacrifice = 4/10 x 1/2 = 4/20 to C
C’s gain = 1/20 x 4/20 = 5/20

Therefore,
A’s New Share = 5/10 – 1/20 = 10 – 1/20 = 9/20
B’s New Share = 4/10 – 4/20 = 8 – 4/20 = 4/20
C’s New Share = 1/10 + 5/20 = 5 + 2/20 = 7/20

Therefore, New Ratio of A, B and C = 9: 4: 7