A and B share profits in the ratio \(13:7\). C is admitted into the partnership for a \(\frac{1}{4}\) share of the profits. A and B sacrifice this share in the ratio \(3:2\). What will be B’s new share of profit?

Correct answer: \(\frac{1}{4}\)

C’s required share is \(\frac{1}{4}\). Total sacrifice by A and B is also \(\frac{1}{4}\). Since sacrifice ratio \(A:B=3:2\), B sacrifices \(\frac{2}{3+2}\times \frac{1}{4}=\frac{2}{5}\times \frac{1}{4}=\frac{2}{20}=\frac{1}{10}\). B’s original share is \(\frac{7}{13+7}=\frac{7}{20}\). So B’s new share \(=\frac{7}{20}-\frac{1}{10}=\frac{7}{20}-\frac{2}{20}=\frac{5}{20}=\frac{1}{4}\).