## 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.

SOLUTION

Old Ratio (A, B and C)  =  4 : 3 : 2
B retires from the firm.
His profit share  =  3/9

Case (a) B gives his share to A and C in their original ratio.
Original Share (A and C) = 4 : 2
Share of mohan taken by A = 3/9 × 4/6 = 12/54
Share of mohan taken by B = 3/9 × 2/6 = 6/54

New Ratio = Old Ratio + Share acquired from B
A‘s new share = 4/9+12/54 = 24+12/54 = 36/54
B‘s new share = 2/9+6/54 = 12+6/54 = 18/54
∴ New Profit Ratio (A and C) = 36: 18 or 2: 1

Case (b) B gives his share to A and C in equal proportion.
Share taken by A and C = 3/9 × 1/2 = 3/18 each

New Ratio  =  Old Ratio + Share acquired from B
A‘s new share =  4/9+3/18  = 8+3/18 = 11/18
C‘s new share =  2/9+3/18  = 4+3/18 = 7/18
∴ New Profit Ratio (A and C) = 11 : 7

Case (c) B gives his to A and C in the ratio 3 : 1.
Share taken by A = 3/9 × 3/4 = 9/36
Share taken by B = 3/9 × 1/4 = 3/36

New Ratio  =  Old Ratio + Share acquired from B
A‘s new share = 4/9+9/36  = 16+9/36 = 25/36
C‘s new share = 2/9+ 3/36 = 8+3/36 = 11/36
∴ New Profit Ratio (A and C) = 25 : 11

Case (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 Share = 2/9
∴ New Profit Ratio (A and C) = 7: 2