A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

For the shortest (straight) path the resultant velocity of the boat relative to ground must be perpendicular to the banks, so the across-river component equals width/time = 1 km / 0.25 hr = 4 km/h . The boat’s speed in still water (5 km/h) combines vectorially with the river’s speed; by the Pythagorean relation between components, 5^2 = 4^2 + v_river^2 . Solving gives v_river = sqrt(25 − 16) = 3 km/h. Hence the river’s velocity is 3 km/h, corresponding to option 2.