Bridge and man timings – find train length A train crosses a 150 m bridge in 15 s and a man (standing) in 9 s at uniform speed. What is the length of the train?
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A225 m
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B200 m
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C135 m
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D90 m
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ENone of these
Answer
Correct Answer: 225 m
Explanation
Introduction / Context:Two timings allow solving for both the train length and speed. The man is a point obstacle (distance = train length). The bridge timing includes both train and bridge lengths.
Given Data / Assumptions:
- Bridge length = 150 m.
- t_bridge = 15 s; t_man = 9 s.
- Uniform speed.
Concept / Approach:Let v be speed in m/s and L the train length. From man: L = v * 9. From bridge: L + 150 = v * 15. Solve the two linear equations for L.
Step-by-Step Solution:
From man: L = 9vFrom bridge: 9v + 150 = 15v ⇒ 6v = 150 ⇒ v = 25 m/sTherefore L = 9 * 25 = 225 mVerification / Alternative check:Bridge check: 225 + 150 = 375 m; at 25 m/s, time = 15 s. Man check: 225 m at 25 m/s is 9 s. Both match.
Why Other Options Are Wrong:200 m, 135 m, 90 m: None satisfies both timing equations simultaneously.
Common Pitfalls:Mixing which timing corresponds to which distance; remember man → distance = L, bridge → distance = L + 150.
Final Answer:225 m