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