A boatman goes 6 km upstream and return to the starting point in 2 hrs. If the speed of current is 4 km/hr, then find the speed of boat in still water.

8 km/hr

Let the speed of boat in still water =u km/hr

and the speed of current = v km/hr = 4 km/hr

Speed of boat in downstream = u + v

Speed of boat in upstream = u - v

Now ATQ,

\(\frac{6}{u + v}\) +  \(\frac{6}{u - v}\) = 2 hrs

\(\frac{6}{u + 4}\) + \(\frac{6}{u - 4}\) =  2 hrs

Checking options,  u = 8 satisfies the above eq.

Speed of boat in still water = 8 km/hr