A man crosses a river in a boat. If he cross the river in minimum time he takes 10 minutes with a drift 120 m. if he crosses the river taking shortest path. He takes 12.5 minute find

(a) width of the river

(b) velocity of the boat with respect to water

(c) speed of the current

Let the velocity of man w.r.t. ground = V_m

Velocity of river w.r.t ground = V_r

Let width of river = D

Case 1. Shortest path

 Shortest path will be the width of the river  

Let the man cross the river at an angle α with the width of the river to reach along the shortest path

1. Thus width of river = 200 m
2. Speed of the boat w.r.t. ground = 0.33 m/s, yourself find out the speed of the boat w.r.t. water in two cases.
3. Speed of the current = 0.2 m/s