Question

A and B are partners in a firm sharing profits and losses in the ratio of 3:2. C is admitted for $\frac{1}{5}$th share in profits of the firm. Calculate the new profit sharing ratio of the partners if,

(a) C gets it equally from A and B

(b) C gets it from A and B in the ratio of 2:1

(c) C gets it wholly from A

(d) C gets it wholly from B

(e)C gets it $\frac{3}{20}$ from A and $\frac{1}{20}$ from B.

Answer 1

(a) If C gets his share equally from A and B:

Share acquired by C from $A=\frac{1}{2}of\frac{1}{5}=\frac{1}{10}$

Share acquired by C from $B=\frac{1}{2}of\frac{1}{5}=\frac{1}{10}$

Hence, A's new share $=\frac{3}{5}-\frac{1}{10}=\frac{6-1}{10}=\frac{5}{10}$

B's new share $=\frac{2}{5}-\frac{1}{10}=\frac{4-1}{10}=\frac{3}{10}$

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

New Ratios $=\frac{5}{10}:\frac{3}{10}:\frac{1}{5}=\frac{5:3:2}{10}=5:3:2$

(b) If C gets his share from A and B in the ratio of 2:1

Share acquired by C from $A=\frac{2}{3}of\frac{1}{5}=\frac{2}{15}$

Share acquired by C from $B=\frac{1}{3}of\frac{1}{5}=\frac{1}{15}$

Hence, A's new share $=\frac{3}{5}-\frac{2}{15}=\frac{9-2}{15}=\frac{7}{15}$

B's new share $=\frac{2}{5}-\frac{1}{15}=\frac{6-1}{15}=\frac{5}{15}$

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

New Ratios $=\frac{7}{15}:\frac{5}{15}:\frac{1}{5}=\frac{7:5:3}{15}=7:5:3$

(c) If C gets his share wholly from A

Hence, A's new share $=\frac{3}{5}-\frac{1}{5}=\frac{2}{5}$

B's share $=\frac{2}{5}$

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

New Ratios = 2:2:1

(d)If C gets his share wholly from B:

A's share $=\frac{3}{5}$

B's new share $=\frac{2}{5}-\frac{1}{5}=\frac{1}{5}$

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

New Ratios = 3:1:1

(e) If C gets $\frac{3}{20}$ from A and $\frac{1}{20}$ from B

A's new share $=\frac{3}{5}-\frac{3}{20}=\frac{12-3}{20}=\frac{9}{20}$

B's new share $=\frac{2}{5}-\frac{1}{20}=\frac{8-1}{20}=\frac{7}{20}$

C's share $=\frac{3}{20}+\frac{1}{20}=\frac{4}{20}$

New ratios = 9:7:4.