A and B are partners in a business.A invests 1/3 of the capital for 8 months and then he reduces his investment by 50%.At the end of two years, A got 1/4 of the total profit as his share for how much time did B invest his capital ?

A invests 1/3 capital for 8 months, then 1/6 capital (50% reduction) for 16 months (24-8). Total A-units = (1/3)*8 + (1/6)*16 = 8/3 + 16/6 = 16/6 + 16/6 = 32/6. A gets 1/4 profit, so total-units/A-units = 4/1, meaning total-units = 128/6. B-units = total - A = 128/6 - 32/6 = 96/6 = 16. Let B invest 1/3 capital for x months: (1/3)*x = 16, so x=48. But B's capital is 2/3 (A had 1/3), so (2/3)*x = 16 gives x=24 months. Option D correct.