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 $B$ given his share to $A$ and $C$ in the original ratio of $A$ and $C$.
(c) If $B$ gives his share to $A$ and $C$ in equal proportion.
(d) 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

Old ratio (A, B and C) = 4: 3 :2

B retires from the firm.

His profit share = 3/9

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

Original share (A and C) = 4:2

Share taken by A = 3/9 X 4/6 = 12/54

Share taken by C = 3/9 X 2/6 = 6/54

New ratio = Old ratio + Share acquired from B

A's new share = 4/9 + 12/54 = 24/54 + 12/54 = 36/54

C's new share = 2/9 + 6/54 = 12/54 + 6/54 = 18/54

Therefore, new profit ratio (A and C) = 36: 18 or 2:1

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

Share taken by A = 3/9 X 1/2 = 3/18

Share taken by C = 3/9 X 1/2 = 3/18

New ratio = Old ratio + Share acquired from B

A's new share = 4/9 + 3/18 = 8/18 + 3/18 = 11/18

C's new share = 2/9 + 3/18 = 4/18 + 3/18 = 7/18

Therefore, new profit ratio (A and C) = 11 : 7

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

Share taken by A = 3/9 X 3/4 = 9/36

Share taken by C = 3/9 X 1/4 = 3/36

New ratio = Old ratio + Share acquired from B

A's new share = 4/9 + 9/36 =16/36 + 9/36 = 25/36

C's new share = 2/9 + 3/36 = 8/36 + 3/36 = 11/36

Therefore, new profit ratio (A and C)= 25: 11

(d) B gives his share to A only.

A's new share = A's old share + Share of B = 4/9 +3/9 = 7/9

C's new share = 2/9

Therefore, new profit share = (A and C) = 7: 2