Question

A, B and C are partners in a firm sharing profits and losses in the ratio of 4 : 3 : 2. B decides to retire from the firm. Calculate new profit-sharing ratio of A and C in the following circumstances:
(a) If B gives his share to A and C in the original ratio of A and C.
(b) If B gives his share to A and C in equal proportion.
(c) If B gives his share to A and C in the ratio of 3 : 1.
(d) If B gives his share to A only.

Answer 1

b) If B gives his share to A and C in equal proportion.

(c) If B gives his share to A and C in the ratio of 3 : 1.

(d) If B gives his share to A only.

HOPE THIS HELPS ❤️

PLEASEMARK AS BRAINLIEST ❤️❤️

Answer 2

The new profit-sharing ratio of A and C in the given circumstances are calculated below:

Explanation:

Old Ratio $(A, B \text { and } C)=4: 3: 2$

Retiring Partner B's Profit Ratio $=\frac{3}{9}$

(a)  B gives his share in the original ratio to A and C

Old Ratio (A and C) $=4: 2$

B's Share taken by A

$=\frac{3}{9} \times \frac{4}{6}=\frac{12}{54}$

B's Share taken by C

$=\frac{3}{9} \times \frac{2}{6}=\frac{6}{54}$

New Ratio = Old Ratio + B's Share Acquired

$A^{\prime} s=\frac{4}{9}+\frac{12}{54}=\frac{24}{54}+\frac{12}{54}=\frac{36}{54}$

$C^{\prime} s=\frac{2}{9}+\frac{6}{54}=\frac{12}{54}+\frac{6}{54}=\frac{18}{54}$

New Ratio

$(A \text { and } C)=\frac{36}{54}: \frac{18}{54}$

or 2: 1

(b) B gives his Share to A and C in equal proportion

B's Share taken by A

$=\frac{3}{9} \times \frac{1}{2}=\frac{3}{18}$

B's share taken by C

$=\frac{3}{9} \times \frac{1}{2}=\frac{3}{18}$

New Ratio = Old Ratio + B's Share taken up

A's New Share

$=\frac{4}{9}+\frac{3}{18}=\frac{8}{18}+\frac{3}{18}=\frac{11}{18}$

C's New Share

$=\frac{2}{9}+\frac{3}{18}=\frac{4}{18}+\frac{3}{18}=\frac{7}{18}$

New Ratio (A and C) $=11: 7$

(c) B gives his Share to A and C in the Ratio 3: 1

B's Share taken by A

$=\frac{3}{9} \times \frac{3}{4}=\frac{9}{36}$

B's Share taken by C

$=\frac{3}{9} \times \frac{1}{4}=\frac{3}{36}$

New Ratio = Old Ratio + B's taken by Share

$A^{\prime} s=\frac{4}{9}+\frac{9}{36}=\frac{16}{36}+\frac{9}{36}=\frac{25}{36}$

$C^{\prime} s=\frac{2}{9}+\frac{3}{36}=\frac{8}{36}+\frac{3}{36}=\frac{11}{36}$

A and C's New Ratio is 25: 11

(d)  B gives his Share to A only

A's New Share = A's Old Share + Share of B's

$=\frac{4}{9}+\frac{3}{9}=\frac{7}{9}$

C's New Share

$=\frac{2}{9}$

Therefore New Profit Ratio $(A \text { and } C)=7: 2$