A B and C share profits in 3:4:5. A retires and B C acquire his share in 1:2. What will be the gaining ratio?

Correct answer: 1:2

The direct answer is option A, 1:2. A, B and C initially share profit in 3:4:5, so their total parts are 12 and A's share is 3/12. When A retires, the question directly says that B and C acquire A's share in the ratio 1:2. Therefore, B gains one part and C gains two parts; the gaining ratio is 1:2. Option A is correct because it states exactly this additional-share ratio. Option B, 4:5, is the old profit-sharing ratio of B and C, not the ratio in which they gain A's share. Option C, 3:4, uses A's old part and B's old part and does not describe the extra benefit received by B and C. Option D, 1:1, would mean that both partners took equal portions, which the question does not say. The old ratio is needed for finding final shares, but here the gaining ratio is already supplied. Memory cue: gaining ratio means the ratio in which continuing partners take the retiring partner's share.