A and B share profits in the ratio 9:5. C is admitted for a \(\frac{1}{7}\) share of the total profit, which is sacrificed by A and B in the ratio 4:3. What will be the new profit-sharing ratio?

Correct answer: 55:29:14

Since the old ratio is 9:5, A and B had shares \(\frac{9}{14}\) and \(\frac{5}{14}\). C receives \(\frac{1}{7}\), and this is sacrificed in the ratio 4:3; therefore, A sacrifices \(\frac{4}{49}\) and B sacrifices \(\frac{3}{49}\). Their new shares are \(\frac{9}{14}-\frac{4}{49}=\frac{55}{98}\) and \(\frac{5}{14}-\frac{3}{49}=\frac{29}{98}\), while C receives \(\frac{1}{7}=\frac{14}{98}\). Hence, the new profit-sharing ratio is 55:29:14. Exam tip: subtract each existing partner’s sacrificed share from the old share; do not subtract the new partner’s share from the old ratio directly.