A and B share profits in the ratio 8:3. C is admitted for a \(\frac{2}{11}\) share of the profits. The remaining profits will be shared by A and B in the ratio 5:4. What will be A's new share of profit?

Correct answer: \(\frac{5}{11}\)

After C receives \(\frac{2}{11}\), the remaining profit for A and B is \(1-\frac{2}{11}=\frac{9}{11}\). A's fraction of this remainder is \(\frac{5}{5+4}=\frac{5}{9}\). Therefore, A's new share is \(\frac{9}{11}\times\frac{5}{9}=\frac{5}{11}\). The value \(\frac{8}{11}\) results from incorrectly applying the old ratio directly. Exam tip: first calculate the remainder after the incoming partner's share, then multiply it by the relevant fraction of the new ratio.