Question
The downstream speed of a boat is
25% more than its upstream speed. The boat takes 3.2 hours to travel 57.6 km upstream. Which of the following statement(s) is or are true according to the information? I. Speed of stream is 3 km/h II. Time required to cover 108 km in still water is 4 hours III. Time needed to go 72 km downstream and return upstream is 7.2 hoursSolution
ATQ: Upstream speed = 57.6 / 3.2 = 18 km/h Downstream speed = (5/4) × 18 = 22.5 km/h Statement I: Speed of stream = (1/2) × (22.5 − 18) = 2.25 km/h → False Statement II: Speed in still water = (1/2) × (22.5 + 18) = 20.25 km/h Time = 108 / 20.25 ≈ 5.33 hours → False Statement III: Time = (72 / 22.5) + (72 / 18) = 3.2 + 4 = 7.2 hours → True Only statement III is true
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