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X and Y are partners in a firm sharing profits in the ratios of 2 : 1. Z is admitted with a 1/3 profit…

When Z is admitted for a 1/3 share of profits, the remaining share available for existing partners X and Y is 1 − 1/3 = 2/3. Dividing this remaining 2/3 share between X and…

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X and Y are partners in a firm sharing profits in the ratios of 2 : 1. Z is admitted with a 1/3 profit sharing. What will be the new profit sharing ratio of X, Y and Z ?

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When Z is admitted for a 1/3 share of profits, the remaining share available for existing partners X and Y is 1 − 1/3 = 2/3. Dividing this remaining 2/3 share between X and Y in their original ratio of 2:1 gives X's new share = (2/3) × (2/3) = 4/9, Y's new share = (2/3) × (1/3) = 2/9, and Z's share = 1/3 = 3/9, resulting in a new profit-sharing ratio of 4 : 2 : 3.

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