The speed of a boat down the stream is 125% of the speed in still water. If the boat takes 30 minutes to cover 20 km in still water, then how much time (in hours) will it take to cover 15 km upstream?

Given : 

Speed of boat a down the stream is 125% of the speed in still water.

Boat takes 30 minutes to cover 20 km in still water.

Concept Used :

Downstream Speed = D/v + u

Upstream Speed = D/v - u

v = Speed of boat, u = Speed of stream

Calculation : 

⇒ v+ u/v = 125/100 = 5/4

⇒ v = 20/30 × 60 = 40

⇒ 4 unit = 40

⇒ 1 unit = 10

⇒ v + u = 50, v = 40, 

⇒ u = 10

Time = 15/v - u = 15/30 = 1/2

∴ The correct answer is 1/2.

Alternate MethodGiven:

Speed of the boat downstream is 125% of the speed in still water.

Time to cover 20 km in still water = 30 minutes.

Distance to cover upstream = 15 km.

Concept Used:

Speed = Distance / Time

Downstream speed = Speed in still water + Speed of stream

Upstream speed = Speed in still water - Speed of stream

Calculation:

Speed in still water = Distance / Time

⇒ Speed in still water = 20 km / 0.5 hours = 40 km/h

Downstream speed = 125% of speed in still water

⇒ Downstream speed = 1.25 × 40 = 50 km/h

Speed of stream = Downstream speed - Speed in still water

⇒ Speed of stream = 50 - 40 = 10 km/h

Upstream speed = Speed in still water - Speed of stream

⇒ Upstream speed = 40 - 10 = 30 km/h

Time = Distance / Upstream speed

⇒ Time = 15 km / 30 km/h = 0.5 hours = 1/2

∴ The boat will take 0.5 hours to cover 15 km upstream.

Answer: 2) 1/2