The speed of a boat in still water is 10 km/hr. If it can travel 78 km downstream and 42 km upstream in the same time, the speed of the stream is

Let the speed of the stream be x km/hr.
Then,
Speed upstream = (10 - x) km/hr.
Speed down speed = (10 + x) km/hr.
Time taken to travel 78 km downstream = Time taken to travel 42 km upstream
78/(10 + x) = 42/(10 - x)
⇒ 13/(10 + x) = 7/(10 - x)
⇒ 130 - 13x = 70 + 7x
⇒ 20x = 60
⇒ x = 60/20
⇒ x = 3 km/hr.