A, B, and C are partners sharing profits in 9 : 6 : 5. D is admitted into partnership. A sacrifices 1/3rd of his share, B sacrifices 1/20th from his share, and C sacrifices 1/5th of his share in favour of D. The New profit-sharing ratio will be ______.

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A, B, and C are partners sharing profits in 9 : 6 : 5. D is admitted into partnership. A sacrifices $\frac{1}{3}$rd of his share, B sacrifices $\frac{1}{20}$th from his share, and C sacrifices $\frac{1}{5}$th of his share in favour of D. The New profit-sharing ratio will be 6 : 5 : 4 : 5. Explanation: Calculate the Sacrifice Ratio: A sacrifices $\frac{1}{3}$rd of his share. A’s sacrifices = $\frac{9}{20}$ xx $\frac{1}{3}$ = $\frac{9}{60}$ A sacrifices $\frac{1}{20}$ from his share. This is an absolute amount, not a fraction of his share. B’s sacrifices = $\frac{1}{20}$ C’s sacrifices = $\frac{1}{5}$of his share. C’s sacrifices = $\frac{5}{20}$ xx $\frac{1}{5}$ = $\frac{5}{100}$ To combine these fractions, we find a common denominator. A’s Sacrifice = $\frac{9}{60}$ = (9 xx 5)/(60 xx 5) = $\frac{45}{300}$ B’s Sacrifice = $\frac{1}{20}$ = (1 xx 15)/(20 xx 15) = $\frac{15}{300}$ C’s sacrifices = $\frac{5}{100}$ = (5 xx 3)/(100 xx 3) = $\frac{15}{300}$ The Sacrifice Ratio of A, B, and C = $\frac{45}{300}$ : $\frac{15}{300}$ : $\frac{15}{300}$ or 45 : 15 : 15 Calculate the New Share for Each Partner: A’s New Share = $\frac{9}{20}$ - $\frac{45}{300}$ = `(9 xx 15)/(20 xx 15) - $\frac{45}{300}$ = $\frac{135}{300}$ - $\frac{45}{300}$ = $\frac{90}{300}$ B’s New Share = $\frac{6}{20}$ - $\frac{15}{300}$ = (6 xx 15)/(20 xx 15) - $\frac{15}{300}$ = $\frac{90}{300}$ - $\frac{15}{300}$ = $\frac{75}{300}$ C’s New Share = $\frac{5}{20}$ - $\frac{15}{300}$ = (5 xx 15)/(20 xx 15) - $\frac{15}{300}$ = $\frac{75}{300}$ - $\frac{15}{300}$ = $\frac{60}{300}$ C’s Share = $\frac{45}{300}$ + $\frac{15}{300}$ + $\frac{15}{300}$ = $\frac{75}{300}$` The New Profit Sharing Ratio of A, B, C, D = `$\frac{90}{300}$ : $\frac{75}{300}$ : $\frac{60}{300}$ : $\frac{5}{300}$` We can simplify this ratio by dividing all numbers by their greatest common divisor, which is 15. The New Profit Sharing Ratio of A, B, C, D = $\frac{6}{20}$ : $\frac{5}{20}$ : $\frac{4}{20}$ : $\frac{5}{20}$ or 6 : 5 : 4 : 5

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