A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

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Q: 147 (IAS/1997)
A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is

question_subject: 

Science

question_exam: 

IAS

stats: 

0,12,11,8,12,2,1

keywords: 

{'velocity': [0, 2, 2, 6], 'boat': [0, 2, 0, 1], 'river water': [0, 2, 1, 2], 'shortest possible path': [0, 1, 0, 0], 'river': [4, 0, 1, 2], 'speed': [0, 1, 2, 0], 'km': [0, 0, 2, 1], 'water': [65, 15, 80, 129], 'minutes': [0, 0, 1, 1], 'width': [0, 2, 1, 1]}

The question is about finding the velocity of the river water. The boat travels at 5 km/hr in still water and crosses a 1 km wide river in 15 minutes. When the river flows, its speed affects the boat`s resulting speed.

Option 1: This would mean the river`s velocity is 1 km/hr. Then, in 15 minutes (which is 0.25hr), the boat would have been carried 0.25km downstream by the river, and it doesn`t align with shortest path concept.

Option 2: This suggests the river`s velocity is 3 km/hr, leading to the boat drifting 0.75km downstream in 15 minutes. This is also inconsistent with the shortest path.

Option 3: This implies the river`s velocity is 4 km/hr, and in 15 min, the boat would have been carried 1 km downstream, meaning it would have travelled more than necessary.

Option 4: The correct answer. It means the river`s velocity is 2 km/hr. With this, the boat can cross the river along the shortest path in given time, confirming that river`s velocity is 2 km/hr.

This dissection explains why option 4 is the correct answer and why the other