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.

Answer 1

Solution:

Calculation of New Profit Sharing Ratio

Case 1: C acquires 115th Share from A.

Given Old Ratio between A :B: C. 5 : 4: 1

C acquires $\frac{1}{5}$ th from A  

A's sacrifice = $\frac{1}{5}$

A= $\frac{5}{10} - \frac{1}{5}$ =  $(\frac{5}{10}) - (\frac{2}{10})$ = $\frac{3}{10}$

B =  $\frac{4}{10}$

C = $\frac{1}{10} + \frac{1}{5}$ = $(\frac{1}{10}) + (\frac{2}{10})$ = $\frac{3}{10}$

Case.2 : C acquires 1/56 Share equally from A and B.

Given Old Ratio A :B: C. 5 : 4:1  

C acquires $\frac{1}{5}$ th share equally from A and B.  

A's sacrifice =  $\frac{1}{10}$

B's sacrifice = $\frac{1}{10}$  

C's gain = $\frac{1}{5}$

A = $\frac{5}{10} - \frac{1}{10}$ = $\frac{4}{10}$

B =  $\frac{4}{10} - \frac{1}{10}$ = $\frac{3}{10}$

C = $\frac{1}{10} + \frac{1}{5}$ = $(\frac{1}{10}) + (\frac{2}{10})$ = $\frac{3}{10}$

A : B: C -= 4: 3 : 3

Case: 3

A, B and C will share future profits and losses equally.

Given: Old Ratio A:B:C = 5:4:1

            New Ratio A:B:C = 1: 1 :1  

A =$\frac{5}{10} - \frac{1}{3}$ = $(\frac{15}{30}) - (\frac{10}{30})$ =  $\frac{5}{30}$ (Sacrifice)

B = $\frac{4}{10} - \frac{1}{3}$ = $(\frac{12}{30}) - (\frac{10}{30})$ =  $\frac{2}{30}$ (Sacrifice)

C = $\frac{1}{10} - \frac{1}{3}$ = $(\frac{3}{30}) - (\frac{10}{30})$ = $-\frac{7}{30}$ (gain)

Case: 4

C acquires 1/106 Share of A and 1/2 share of B.

Given Old Ratio A:B:C = 5:4:1  

A's sacrifice to C = $\frac{5}{10} X \frac{1}{10}$ = $\frac{1}{20}$

B's sacrifice to C = $\frac{4}{10} X \frac{1}{2}$  = $\frac{4}{20}$

C's gain = $\frac{1}{20} + \frac{4}{20}$ = $\frac{5}{20}$

A= $\frac{5}{10} - \frac{1}{20}$ = $(\frac{10}{20}) - (\frac{1}{20})$ = $\frac{9}{20}$

B =  $\frac{4}{10} - \frac{4}{20}$ = $(\frac{8}{20}) - (\frac{4}{20})$ = $\frac{4}{20}$

C = $\frac{1}{10} + \frac{5}{20}$ = $(\frac{2}{20}) + (\frac{5}{20})$ =  $\frac{7}{20}$

A:B:C = 9:4:7

Answer 2

Answer:

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