A train crosses a 100 m platform in 30 s at 45 km/h. How long will the same train take to cross a single electric pole? (Find train length first.)
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A8 seconds
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B30 seconds
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C52 seconds
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DNone of these
Answer
Correct Answer: None of these
Explanation
Introduction / Context:Crossing a platform requires the train to cover its own length plus the platform length. Crossing a pole requires only the train’s own length. We compute the train length from the platform scenario and then find the time for the pole case.
Given Data / Assumptions:
- Platform length = 100 m.
- Speed v = 45 km/h = 12.5 m/s.
- Time over platform = 30 s.
Concept / Approach:Total distance over platform = (train length + platform length) = v * t. Then train length = (v * t − platform length). For a pole, time = (train length) / v.
Step-by-Step Solution:
v = 45 km/h = 45 * 5/18 = 12.5 m/s.Distance over platform = 12.5 * 30 = 375 m.Train length = 375 − 100 = 275 m.Time to cross pole = 275 / 12.5 = 22 s.Verification / Alternative check:Check platform case: (275 + 100)/12.5 = 375/12.5 = 30 s, consistent.
Why Other Options Are Wrong:8 s, 30 s, and 52 s do not match the computed 22 s. Therefore “None of these” is correct here.
Common Pitfalls:Forgetting that platform adds extra length, or failing to convert km/h to m/s correctly.
Final Answer:None of these