A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?

Correct Option: (d) 3 : 1

Let the speed of the man in still water be u and the speed of the current (stream) be v. Speed downstream = u + v. Speed upstream = u - v. Let the fixed distance be d. According to the problem, the time taken downstream is half the time taken upstream: Time downstream = (1/2) × Time upstream. Therefore, d / (u + v) = (1/2) × [d / (u - v)]. Cancelling d and cross-multiplying gives: 2(u - v) = 1(u + v). Expanding this: 2u - 2v = u + v. Rearranging terms: 2u - u = v + 2v, which simplifies to u = 3v. We need the ratio of the speed in still water (u) to the speed of the current (v): u / v = 3 / 1, i.e., 3 : 1. Option (d) is correct.