A and B share profits in the ratio \(3:2\). C is admitted for a \(\frac{1}{4}\) share of profits, which is sacrificed by A and B in the ratio \(1:3\). What will be the new profit-sharing ratio of A, B and C?

Correct answer: A : B : C = 43 : 17 : 20

C receives \(\frac{1}{4}\) of the profits, and A and B sacrifice this share in the ratio \(1:3\). Therefore, A’s sacrifice is \(\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}\), while B’s sacrifice is \(\frac{1}{4}\times\frac{3}{4}=\frac{3}{16}\). Their old shares are A = \(\frac{3}{5}\) and B = \(\frac{2}{5}\). Hence, A’s new share is \(\frac{3}{5}-\frac{1}{16}=\frac{43}{80}\), B’s new share is \(\frac{2}{5}-\frac{3}{16}=\frac{17}{80}\), and C’s share is \(\frac{1}{4}=\frac{20}{80}\). Thus, the new ratio is \(43:17:20\). Option B is incorrect because it retains the old shares of A and B without deducting their sacrifices. Exam tip: Distribute the incoming partner’s share according to the sacrifice ratio and subtract those amounts from the old partners’ shares.