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Question
X, Y and Z are partners sharing profits & losses in the ratio of 4/9:1/3:2/9 respectively. Y retires and surrenders 13/72nd from his share in favour of X and the remaining In support of Z. The gaining ratio will be ______.
X, Y and Z are partners sharing profits & losses in the ratio of 4/9:1/3:2/9 respectively. Y retires and surrenders 13/72nd from his share in favour of X and the remaining In support of Z. The gaining ratio will be ______.
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Solution
The correct option is C 13 : 11
Old ratio (X,Y and Z) = 4/9 : 1/3 : 2/9 Y's share = 1/3Share of Y taken by X = (1/3) * (13/72) = 13/216Share of Y taken by Z = (1/3) * (11/72) = 11/216New ratio = Old profit share + share taken from YX = (4/9) + (13/216) = 109/216Z = (2/9) + (11/216) = 59/216Gaining ratio = New ratio - old ratioX = (109/216) - (4/9) = 13/216Z = (59/216) - (2/9) = 11/216Therefore, gaining ratio = 13 : 11
Old ratio (X,Y and Z) = 4/9 : 1/3 : 2/9
Y's share = 1/3
Share of Y taken by X = (1/3) * (13/72) = 13/216
Share of Y taken by Z = (1/3) * (11/72) = 11/216
New ratio = Old profit share + share taken from Y
X = (4/9) + (13/216) = 109/216
Z = (2/9) + (11/216) = 59/216
Gaining ratio = New ratio - old ratio
X = (109/216) - (4/9) = 13/216
Z = (59/216) - (2/9) = 11/216
Therefore, gaining ratio = 13 : 11
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