A and B share profits in the ratio 7:8. C is admitted for a 1/3 share of profits, and the new profit-sharing ratio of A and B is fixed at 3:2. What is B’s sacrificing ratio?

Correct answer: \(\frac{4}{15}\)

After C’s admission, the profit share left for A and B is \(1-\frac{1}{3}=\frac{2}{3}\). Under the new ratio 3:2, B’s new share is \(\frac{2}{3}\times\frac{2}{5}=\frac{4}{15}\). B’s old share was \(\frac{8}{15}\), so B’s sacrifice is \(\text{old share}-\text{new share}=\frac{8}{15}-\frac{4}{15}=\frac{4}{15}\). The exam rule is to subtract the incoming partner’s reduced share from the old partner’s share, not the reverse.