A and B share profits in the ratio 7:5. C is admitted for a \(\frac{1}{3}\) share of the profits. After C’s admission, the new mutual ratio of A and B is 4:3. What will be the firm’s new profit-sharing ratio?

Correct answer: A : B : C = 8 : 6 : 7

After giving C a \(\frac{1}{3}\) share, \(\frac{2}{3}\) of the profits remains for A and B. This remaining share is divided between them in their new mutual ratio of 4:3. Thus, A’s share is \(\frac{2}{3} \times \frac{4}{7}=\frac{8}{21}\), and B’s share is \(\frac{2}{3} \times \frac{3}{7}=\frac{6}{21}\). C’s share is \(\frac{1}{3}=\frac{7}{21}\). Therefore, the new profit-sharing ratio is 8:6:7. Exam tip: Use the new mutual ratio to divide the remaining profit; the old 7:5 ratio is not used at this stage.