#### Question

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

Calculation of new profit sharing ratio

**Case 1:**

A : B : C = 5 : 4 : 1 (Old ratio)

C aquires `1/5 "th"` from A

A's sacrifice = `1/5`

C's gain = `1/5`

A = `5/10 - 1/5 = (5-2)/10 = 3/10`

B = `4/10`

C = `1/10 + 1/5 = (1=2)/10 = 3/10`

A : B : C = 3 : 4 : 3

**Case 2:**

A : B : C = 5 : 4 : 1 (Old ratio)

C aquires `1/5 "th"` share equally from A

A's sacrifice = `1/10`

B's sacrifice = `1/10`

C's gain = `1/5`

A = `5/10 - 1/10 = (5-1)/10 = 4/10`

B = `4/10 - 1/10 = (4-1)/10 = 3/10`

C = `1/10 + 1/5 = (1+2)/10 = 3/10`

A : B : C = 4 : 3 : 3

**Case 3: **

A : B : C = 5 : 4 : 1 (Old ratio)

A : B : C = 1 : 1 : 1 (New ratio)

A = `5/10 - 1/3 = (15-10)/30 = 5/30` (Sacrifice)

B = `4/10 - 1/3 = (12-10)/30 = 2/30` (sacrifice)

C = `1/10 - 1/3 = (3-10)/30 = -7/30` (gain)

**Case 4:**

A : B : C = 5 : 4 : 1 (Old ratio)

A's sacrifice to C = `5/10 xx 1/10 = 1/20`

B's sacrifice to C = `4/10 xx 1/2 = 4/20`

C's gain = `1/20 + 4/20 = 5/20`

A = `5/10 - 1/20 = (10-1)/20 = 9/20`

B = `4/10 - 4/20 = (8-4)/20 = 4/20`

C = `1/10 + 5/10 = (2+5)/20 = 7/20`

A : B : C = 9 : 4 : 7