Correct Answer - Option 1 : 15
Given:
A boat speed in still water = 20 km/hr
Distance travelled by boat downstream = 75 km
Distance travelled by boat upstream = 75 km
Total time of travel for both upstream and downstream = 8 hours
Formula:
Upstream speed = (u − v) km/hr
Downstream speed = (u + v) km/hr
where “u” is the speed of the boat in still water and “v” is the speed of the stream
Speed of Boat in Still Water = 1/2 (Downstream Speed + Upstream Speed)
Speed of Stream = 1/2 (Downstream Speed – Upstream Speed)
Calculation:
Let the speed of the stream be x km/hr
Upstream Speed = 20 - x
Downstream Speed = 20 + x
⇒ 75/(20 + x) + 75/(20 - x) = 8
⇒ 75(20 - x + 20 + x)/(400 - x2) = 8/75 = 375
⇒ 400 - x2 = 375
⇒ x = 5
The Upstream speed = 20 - 5 ⇒ 15 km/h
∴ The upstream speed is 15 km/h.