**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**

**B gives his share to A and C in equal proportion.**

__Case (b)__Share taken by A and C = 3/9 × 1/2 = 3/18 each

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

New Ratio = Old Ratio + Share acquired from B

New Ratio = Old Ratio + Share acquired from B

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

**∴ New Profit Ratio (A and C) = 11 : 7**

**B gives his to A and C in the ratio 3 : 1.**

__Case (c)__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**

**B gives his share to A only.**

__Case (d)__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**