A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the oat in still water and the speed of the stream.

Speed = distance/time

Let the speed of boat be ‘a’ and speed of stream be ‘b’

Relative speed of boat going upstream = a – b

Relative speed of boat going downstream = a + b

Given, boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time

------- (1)

Also, ------ (2)

Equating (1) and (2), we get

⇒ 8/(a + b) = 4/(a – b)

⇒ a = 3b

Substitute value of a in eq1

⇒ 12/2b + 40/4b = 8

⇒ 16/b = 8

⇒ b = 2 km/hr

Thus, a = 6 km/hr.