In a partnership business, B's capital was one fourth of A's. If after 5 months, B withdrew one fourth of his capital and after three more months, A withdrew half of his capital. What is the profit-sharing ratio of A and B?

Let A's capital = 4x, so B's capital = x (one fourth). After 5 months, B withdraws 1/4, so B's remaining capital = 3x/4. After 3 more months (8 months total), A withdraws half, so A's remaining capital = 2x. This continues till 12 months. Profit ratio = (capital × time): A = 4x×8 + 2x×4 = 32x + 8x = 40x. B = x×5 + (3x/4)×7 = 5x + 21x/4 = 20x/4 + 21x/4 = 41x/4. Ratio A:B = 40x : 41x/4 = 40 : 41/4 = 160 : 41.