**SOLUTION**

**(a)**Old Ratio (W, X, Y and Z) = of 1/3; 1/6: 1/3; 1/6 or 2 : 1 : 2 : 1

New Ratio (W, X and Z) = 1 : 1 : 1

**Gaining Ratio = New Ratio − Old Ratio**

W’s Gain = 1/3-2/6 = 2-2/6 = 0/6

X’s Gain = 1/3-1/6 = 2-1/6 = 1/6

Z’s Gain = 1/3-1/6 = 2-1/6 = 1/6**∴Gaining Ratio = 0: 1: 1**

**(b)**Old Ratio (A, B and C) = 4: 3: 2

C’s Profit Share = 2/9

A acquires 4/9 of C’s Share and remaining share is acquired by B.

Share acquired by A = 2/9 × 4/9 = 8/81

Share acquired by B = C’s share- Share acquired by A = 2/9-8/81 = 10/81**New Profit Share = Old Profit Share + Share acquired from C**

A’s new share = 4/9+8/81 = 36+8/81 = 44/81

B’s new share = 3/9+10/81 = 27+10/81 = 37/81

New Profit Ratio A and B = 44: 37

**Gaining Ratio = New Ratio − Old Ratio**

A’s Gain = 44/81-4/9 = 44-36/81 = 8/81

B’s Gain = 37/81-3/9 = 37-27/81 = 10/81**∴Gaining Ratio = 8: 10 or 4: 5**