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(a) W, X, Y and Z are partners sharing profits and losses in the ratio of 1/3, 1/6, 1/3 and 1/6 respectively. Y retires and W, X and Z decide to share the profits and losses equally in future. Calculate gaining ratio. (b) A, B and C are partners sharing profits and losses in the ratio of 4: 3: 2. C retires from the business. A is acquiring 4/9 of C’s share and balance is acquired by B. Calculate the new profit-sharing ratio and gaining ratio.

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


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