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Question

A train travelling at 60 km/h overtakes another train travelling at 42 km/h. Assuming each car to be 50 m long and initially train A to be just behind the train B, the total distance train A will cover to overtake train B is closest to

A
180 m
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B
383 m
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C
343 m
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D
250 m
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Solution

The correct option is B 383 m
Velocity of train A=60 km/h
=60×518 ms1=503 ms1
Velocity of train B=42 km/h
=42×518 ms1=353 ms1
Relative velocity of train A w.r.t B=503353=5 ms1
train A overtakes train B when distance covered relatively by car A is 100 m i.e. the sum of the length of the trains,
Using Srel=urelt+12arelt2
100=5t+0
t=20 s
So, the distance required to overtake would be displacement of faster train which is A + Length of train A
Road distance required =vAt+50=503×20+50
383 m

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