A and B share profits in the ratio 6:7. C is admitted for a \(2/13\) share of the total profit, and the remaining profit is shared by A and B in their old ratio. What is the new profit-sharing ratio?

Correct answer: 66:77:26

C receives \(2/13\), so the remaining share for A and B is \(1-2/13=11/13\). Sharing this remainder in the old ratio 6:7 gives A \((11/13)×(6/13)=66/169\) and B \((11/13)×(7/13)=77/169\). C’s share is \(2/13=26/169\). Therefore, the new ratio is 66:77:26. Exam tip: first subtract the incoming partner’s share from 1, then distribute the remainder in the old ratio.