Two trains A and B are running on parallel tracks in same direction. Length of train A is twice that of train B. Both trains take an equal amount of time to cross a pole individually. If speed of train B is 60 km/hr and its length is 400 metres, then how much time will train A take to completely overtake train B?

Two trains A and B are running on parallel tracks in same direction. Length of train A is twice that of train B. Both trains take an equal amount of time to cross a pole individually. If speed of train B is 60 km/hr and its length is 400 metres, then how much time will train A take to completely overtake train B?
1). 24 seconds
2). 36 seconds
3). 48 seconds
4). 54 seconds

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Guest · Answer 1 · 2019-07-07 23:33:48

As per the problem statement,

Length of train B = 400 m

Since, length of train A is twice the length of train B,

⇒ Length of train A = 2 × 400 m = 800 m

When a train crosses a pole, it covers a distance equal to its length (as length of pole can be neglected when compared to length of train).

Both trains take same time to cross the pole, and we know that

Time=Distance/Speed

∴ (Distance covered by train A)/(Speed of train A) = (Distance covered by train B)/(Speed of train B)

⇒ Speed of train A = [800 m × 60 km/hr]/400 m = 120 km/hr

Now, the trains are moving in the same direction and faster train will overtake the slower train. In doing so, the faster train will cover a distance that is equal to the sum of lengths of both trains.

Distance covered = Length of train A + Length of train B = 800 m + 400 m = 1200 m

The relative speed of faster train A, with respect to, slower train B will be given by

Speed of train A w.r.t. train B = Speed of train A – Speed of train B = 120km/hr – 60 km/hr = 60 km/hr

This speed when converted to the units of m/sec, will be [60 × (5/18)] m/sec = (50/3) m/sec

We know,
Time=Distance/Speed

Time taken $(= \;\frac{{1200\;m}}{{\left( {\frac{{50}}{3}} \right)m/sec}})$ = 72 seconds

∴ Time taken by train A to overtake train B = 72 seconds

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