Question : A and B are partners in a firm sharing profits in a ratio of 7: 3. C is admitted as a new partner. A sacrifices 2 / 7 th of his share in profits in favour of C and B 1 / 7 th of his share in favour of C. The new profit-sharing ratio between A, B and C will be
Option 1: 39: 11: 30
Option 2: 50: 11: 30
Option 3: 35: 18: 17
Option 4: None of the above
Correct Answer: 35: 18: 17
Solution : Answer = 35: 18: 17 A's old share $=\frac{7}{10}$; Asurrenders $\frac{2}{7}$ th of $\frac{7}{10}$ in fayour of C, i. e., $\frac{2}{7} \times \frac{7}{10}=\frac{2}{10}$ (It means that A has surrendered $\frac{2}{10}$ out ofhis share in favour of C ) B's old share $=\frac{3}{10}$; B suirenders $\frac{1}{7}$ th of $\frac{3}{10}$ in favour of C, i. e., $\frac{1}{7} \times \frac{3}{10}=\frac{3}{70}$ (It means that B has surrendered $\frac{3}{70}$ out ofhis share in favour of C) Calculation of New Ratios: A's new share after simendenng $\frac{2}{10}$ in favour of C=$\frac{7}{10}-\frac{2}{10}=\frac{5}{10}$ B's share after simendenng $\frac{3}{70}$ in favour of C=$\frac{3}{10}-\frac{3}{70}=\frac{21-3}{70}=\frac{18}{70}$
C's share is the total of $\frac{2}{10}$ from A and $\frac{3}{70}$ from B=$\frac{2}{10}+\frac{3}{70}=\frac{14+3}{70}=\frac{17}{70}$
Hence, New ratio of A, B and C=$\frac{5}{10}: \frac{18}{70}: \frac{17}{70}=\frac{35: 18: 17}{70}=35: 18: 17$ Hence, the correct option is 3.
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