A and B share profits in the ratio \(5:6\). New partner C is given \(\frac{1}{4}\) of the total profit. If the remaining profit is shared between A and B in their old ratio, what will be the new profit-sharing ratio?

Correct answer: \(15:18:11\)

C receives \(\frac{1}{4}\) of the total profit, so the remaining profit for A and B is \(\frac{3}{4}\). The sum of A and B’s old ratio is 11. Therefore, A’s share is \(\frac{3}{4}\times\frac{5}{11}=\frac{15}{44}\), and B’s share is \(\frac{3}{4}\times\frac{6}{11}=\frac{18}{44}\). C’s share is \(\frac{1}{4}=\frac{11}{44}\). Hence, the new ratio is \(15:18:11\). Exam tip: First calculate the balance share, then distribute it among the old partners in their old ratio.