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A man and train running at speed of 9 km/h and 72 km/h cross each other in 30 seconds in same direction. Train crosses another train in the same direction with a speed of 18 km/h in 40 seconds, then find the length of another train.
  • a)
    600 m
  • b)
    750 m
  • c)
    450 m
  • d)
    250 m
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A man and train running at speed of 9 km/h and 72 km/h cross each othe...
Let the length of the train be A m.
Speed of man = 9 × 5/18 = 2.5 m/sec
Speed of train = 72 × 5/18 = 20m/sec
Given,
Relative speed = 20 – 2.5 = 17.5
⇒ A/17.5 = 30
⇒ A = 525 m
Let the length of another train be B m.
Speed of another train = 18 × 5/18 = 5 m/sec
Relative speed = 20 – 5 = 15
⇒ B/15 = 40
⇒ B = 600 m
∴ The length of another train is 600 m.
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Most Upvoted Answer
A man and train running at speed of 9 km/h and 72 km/h cross each othe...
Understanding the Problem
To solve the problem, we need to analyze the scenarios involving speed, time, and distance.
Scenario 1: Train and Man Crossing Each Other
- Speed of Man: 9 km/h
- Speed of Train: 72 km/h
- Relative Speed: Since they are moving in the same direction, we subtract the speeds:
Relative Speed = 72 km/h - 9 km/h = 63 km/h
- Time Taken to Cross: 30 seconds
- Distance Covered (Length of Train):
Convert speed to m/s: 63 km/h = (63 * 1000) / 3600 = 17.5 m/s
Distance = Speed × Time = 17.5 m/s × 30 s = 525 m
Scenario 2: Train Crossing Another Train
- Speed of First Train: 72 km/h
- Speed of Second Train: 18 km/h
- Relative Speed: Since they are also moving in the same direction:
Relative Speed = 72 km/h - 18 km/h = 54 km/h
- Time Taken to Cross: 40 seconds
- Length of Second Train:
Convert speed to m/s: 54 km/h = (54 * 1000) / 3600 = 15 m/s
Distance = Speed × Time = 15 m/s × 40 s = 600 m
Conclusion
Based on the calculations, the length of the second train is found to be 600 meters. Hence, the correct answer is option 'A'.
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