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A boat with a speed of 20 km/hr in still water travels 75 km downstream and returns in a total time of 8 hours. What is the upstream speed in km/hr?
1. 15
2. 16
3. 20
4. 25

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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 - x= 375

⇒ x = 5

The Upstream speed = 20 - 5 ⇒ 15 km/h

∴ The upstream speed is 15 km/h.

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