Problems on Trains

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Problems on Trains


  • a km/hr = m/s
  • a m/s = km/hr
  • Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.
  • Time taken by a train of length l metres to pass a stationary object of length b metres is the time taken by the train to cover (l + b) metres.
  • Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed = (u – v) m/s.
  • Suppose two trains or two bodies are moving in the opposite direction at u m/s and v m/s, then their relative speed is = (u + v) m/s.
  • If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other =
  • If two trains of length a metres and b metres are moving in same directions at u m/s and v m/s, then time taken by the faster train to cross the slower train =
  • If two trains start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then (A’s speed) : (B’s speed) = ()

Ques1. A train moves with a speed of 108 kmph. Its speed in metres per second is:

  • 8 b.) 18                     c.) 30                     d.) 38.8                       e.) None of these

Explanation: Answer is C


108 kmph =  m/s = 30 m/sec

Ques2. A train 280 m long, running with a speed of 63 km/hr will pass a tree in:

  • 15 sec       ) 16 sec                 c.) 18 sec                 d.) 20 sec                   e.) None of these

Explanation: Answer is B

Speed =  m/sec =  m/sec

Time taken =  sec = 16 sec

Ques3. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

  • 120 metres ) 180 metres                 c.) 324 metres                   d.) 150 metres                      e.) None of these

Explanation: Answer is D

Speed =  m/sec =  m/sec

Length of the train = (speed * time) =  m = 150 m

Ques4. A train covers a distance of 12 km in 10 minutes and if it takes 7 seconds to pass a pole, then the length of the train is:

  • 90 m ) 100 m                   c.) 120 m                    d.) 140 m                   e.) None of these

Explanation: Answer is D

Speed =  km/hr =  m/sec = 20 m/sec

Length of the train = (speed * time) = (20 * 7) m = 140 m

Ques5. The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

  • 200 m ) 225 m                   c.) 235 m                     d.) 250 m                    e.) None of these

Explanation: Answer is C

Speed =  m/sec =  m/sec; Time = 30 sec

Let the length of bridge be x metres.

Then,  =  ó 2(140 + x) = 750 ó x = 235 m