A and B share profits in the ratio 13:5. C is admitted for a \(1/9\) share, and the remaining profit is shared in the old ratio. What will be the new profit-sharing ratio?

Correct answer: 52:20:9

C receives \(1/9\) of the total profit, so the remaining share for A and B is \(8/9\). The sum of the old ratio 13:5 is 18. Therefore, A’s share is \((8/9)\times(13/18)=52/81\), and B’s share is \((8/9)\times(5/18)=20/81\). C’s share is \(1/9=9/81\). Hence, the new ratio is \(52:20:9\). For instance, in 104:40:9, C’s share would be \(9/153=1/17\), not \(1/9\), so that option is incorrect. Exam tip: subtract the incoming partner’s share first, then distribute the balance in the old ratio.