A and B share profits in the ratio of 5:1. C is admitted for a 1/3 share, and A and B share the remaining profit in the ratio of 2:1. Which old partner gains?

Correct answer: B gained

C receives 1/3, leaving 2/3 for A and B. Therefore, A’s new share is \(\frac{2}{3}\times\frac{2}{3}=\frac{4}{9}\), while B’s new share is \(\frac{2}{3}\times\frac{1}{3}=\frac{2}{9}\). B’s old share was \(\frac{1}{6}\), so B gains \(\frac{2}{9}-\frac{1}{6}=\frac{1}{18}\). A’s new share, \(\frac{4}{9}\), is lower than A’s old share of \(\frac{5}{6}\), so A sacrifices rather than gains. Exam tip: compare each old partner’s new share with the old share; a positive difference indicates a gain.