A and B are partners sharing profits in the ratio of $5:4$. C is admitted as a partner and he acquires 25% of his share from A. B surrenders $\frac{1}{4}$ th from his share in favour of C. Calculate C's share in profit.

Let C's total share be $X$.C acquires 25% of his share from A, meaning the remaining 75% comes from B.B surrenders $\frac{1}{4}$ from his share. Old ratio of B = $\frac{4}{9}$. Sacrifice by B = $\frac{1}{4}\times \frac{4}{9}=\frac{1}{9}$.This sacrifice by B represents 75% of C's share.$75\%\text{ of }X=\frac{1}{9}⟹\frac{3}{4}\times X=\frac{1}{9}⟹X=\frac{1}{9}\times \frac{4}{3}=\frac{4}{27}$.Wait, "B surrenders 1/4th from his share", wait, if it means total $\frac{1}{4}$ of the firm. Let's recalculate based on standard interpretation:B's sacrifice = $\frac{1}{4}$ from his share directly? Let's check options.Assuming B's sacrifice = $\frac{1}{4}$ of his share = $\frac{1}{4}\times \frac{4}{9}=\frac{1}{9}$.If $\frac{3}{4}X=\frac{1}{9}$, then $X=\frac{4}{27}$.If C gets 25% from A, then A gives $\frac{1}{4}\times \frac{4}{27}=\frac{1}{27}$.Total = $\frac{1}{27}+\frac{3}{27}=\frac{4}{27}$. Not matching options.Alternative interpretation: "B surrenders $\frac{1}{4}$ from his share" means B gives $\frac{1}{4}$ directly.$0.75\times C=\frac{1}{4}⟹C=\frac{1}{3}$. This matches Option C exactly.