A train crosses a pole in 10 s and a 200 m platform in 20 s. What is the length of the train (in metres)?
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A100m
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B200m
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C250m
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D300m
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ENone of these
Answer
Correct Answer: 200m
Explanation
Introduction / Context:Let the train length be L and speed be v (m/s). Passing a pole takes L/v seconds, while passing a platform of length P takes (L + P)/v seconds at the same speed. Using the two given times allows solving for L directly without computing v numerically first.
Given Data / Assumptions:
- Pole time = 10 s ⇒ L = 10v.
- Platform length P = 200 m; platform time = 20 s ⇒ L + 200 = 20v.
Concept / Approach:Eliminate v by substituting L = 10v into the platform equation and solve for L. This exploits the same-speed condition across both scenarios.
Step-by-Step Solution:
L + 200 = 20v and L = 10v ⇒ 10v + 200 = 20v.200 = 10v ⇒ v = 20 m/s.Then L = 10v = 200 m.Verification / Alternative check:Check: time across platform = (L + 200)/v = (200 + 200)/20 = 20 s—consistent.
Why Other Options Are Wrong:100/250/300 m contradict either the pole time or platform time at a single consistent speed.
Common Pitfalls:Assuming 20 s implies double the length only; it is double total distance L + P, not L itself unless computed properly.
Final Answer:200m