Question

(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.

Answer 1

(a)

Old Ratio (W, X, Y and Z) = `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`

`"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 xx 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