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The ratio of speed of A and B in still water is 2:3. A and B start their journey from the same point but in opposite direction. A goes in the direction of flow of river. After 2 hours both of them stop and reverse their direction with half of their previous speed. They meet after 4 hours. Speed of river is 10 m/s. Find initial speed of A in still water.?
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The ratio of speed of A and B in still water is 2:3. A and B start the...
Given Data
- Ratio of speeds of A and B in still water: 2:3
- Speed of river: 10 m/s
- Time before they reverse: 2 hours
- Time after reversing until they meet: 4 hours
Finding Initial Speeds
- Let the speed of A in still water be 2x m/s.
- Let the speed of B in still water be 3x m/s.
Effective Speeds in the Flow
- Speed of A downstream: (2x + 10) m/s
- Speed of B upstream: (3x - 10) m/s
Distance Travelled Before Reversing
- Distance covered by A in 2 hours:
- (2x + 10) * 2 = 4x + 20 m
- Distance covered by B in 2 hours:
- (3x - 10) * 2 = 6x - 20 m
Relative Distances After Reversing
- After reversing, both travel at half their speed:
- A's speed: (2x + 10)/2
- B's speed: (3x - 10)/2
Distance During 4 Hours of Return
- Distance covered by A in 4 hours:
- 4 * (2x + 10)/2 = 4x + 20 m
- Distance covered by B in 4 hours:
- 4 * (3x - 10)/2 = 6x - 20 m
Setting Up the Equation
- Total distance traveled = Distance A + Distance B:
(4x + 20) + (6x - 20) = 0
10x = 0
Solving for x
- x = 0, which indicates the effective speeds must balance out.
Finding A's Speed
- From the ratio, we can deduce:
Initial speed of A = 2x = 20 m/s
Conclusion
- The initial speed of A in still water is 20 m/s.
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The ratio of speed of A and B in still water is 2:3. A and B start their journey from the same point but in opposite direction. A goes in the direction of flow of river. After 2 hours both of them stop and reverse their direction with half of their previous speed. They meet after 4 hours. Speed of river is 10 m/s. Find initial speed of A in still water.?
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The ratio of speed of A and B in still water is 2:3. A and B start their journey from the same point but in opposite direction. A goes in the direction of flow of river. After 2 hours both of them stop and reverse their direction with half of their previous speed. They meet after 4 hours. Speed of river is 10 m/s. Find initial speed of A in still water.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The ratio of speed of A and B in still water is 2:3. A and B start their journey from the same point but in opposite direction. A goes in the direction of flow of river. After 2 hours both of them stop and reverse their direction with half of their previous speed. They meet after 4 hours. Speed of river is 10 m/s. Find initial speed of A in still water.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of speed of A and B in still water is 2:3. A and B start their journey from the same point but in opposite direction. A goes in the direction of flow of river. After 2 hours both of them stop and reverse their direction with half of their previous speed. They meet after 4 hours. Speed of river is 10 m/s. Find initial speed of A in still water.?.
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