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 \( \displaystyle\frac{1}{4} \)th from his share in favour of C. Calculate C’s share in profit.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{1}{3} \)
C's whole share comes from A and B. The question says C takes 25% of his share from A, so the other 75% of his share comes from B. B gives up \( \frac{1}{4} \) of the firm's profit, so this \( \frac{1}{4} \) is 75% of C's share.
C's share × 75/100 = \( \frac{1}{4} \)
C's share = \( \frac{1}{4} \) × \( \frac{100}{75} \) = \( \frac{1}{3} \)
Check: A gives 25% of \( \frac{1}{3} \) = \( \frac{1}{12} \), and B gives \( \frac{1}{4} \) = \( \frac{3}{12} \). Together they give \( \frac{4}{12} \) = \( \frac{1}{3} \), which is C's share.
Note: The wording of this question can be read in another way. If “25% of his share” is taken as 25% of A’s share, A gives \( rac{5}{9} \) × \( rac{1}{4} \) = \( rac{5}{36} \), and with B’s \( rac{1}{4} \) = \( rac{9}{36} \), C would get \( rac{14}{36} \), which is Option (2). But in the sentence “he acquires 25% of his share from A”, the word ‘his’ points to C, the one who acquires, so the reading used above, which gives \( rac{1}{3} \), is the better one.