A and B are partners sharing profits and losses in 3 : 2. They admit C for a $\frac{1}{5}$ th share. In future the ratio between A and B would be 2 : 1. The New profit-sharing ratio will be ______.

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A and B are partners sharing profits and losses in 3 : 2. They admit C for a $\frac{1}{5}$ th share. In future the ratio between A and B would be 2 : 1. The New profit-sharing ratio will be 8 : 4 : 3. Explanation: Determine the Remaining Profit Share: Remaining Share = 1 - $\frac{1}{5}$ = $\frac{4}{5}$ Distribute the Remaining Share between A and B: A’s New Share = $\frac{4}{5}$ xx $\frac{2}{3}$ = $\frac{8}{15}$ B’s New Share = $\frac{4}{5}$ xx $\frac{1}{3}$ = $\frac{4}{15}$ C’s New Share = $\frac{1}{5}$ = (1 xx 3)/(5 xx 3) = $\frac{3}{15}$ The New profit-sharing ratio of A, B, and C = $\frac{8}{15}$ : $\frac{4}{15}$ : $\frac{3}{15}$ or 8 : 4 : 3

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