Tips on Cracking Aptitude Questions on Trains

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2 TIPS on cracking Aptitude Questions on Trains
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Tip 1 Understand the concepts involved in a
train crossing a pole or a platform.

• Time taken by a train of length L to pass a pole
  or standing man or a signal post is equal to the
  time taken by the train to cover distance L.
• Time taken by a train of length L to pass a
  station of length b is the time taken by the
  train to cover the distance (L b).
• Question A train running at the speed of 60
  km/hr crosses a pole in 9 seconds. What is the
  length of the train?
• Solution
• Time taken to cross a pole time taken to cover
  distance equal to its own length.
• Speed of the train in m/s 60 x 5 / 18 (50/3)
  m/s.
• Length of the train Speed of the train x Time
  taken to cross the pole
• 50/3 x 9
• Length of the train 150m.
• Question A train passes a station platform in
  36 sec and a man standing on the platform in 20
  sec. If the speed of the train is 54 km/hr, what
  is the length of the platform?
• Solution
• Speed of the train in m/s 54 x 5 / 18 15m/s.
• Length of the train 15 x 20 300m.
• Distance traveled in 36s 15 x 36 540m. (This
  is the length of the train platform combined)
• Length of the platform (540 200)m 240m.

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Tip 2 For problems on 2 trains, use the concept
of relative velocity

• If two trains of length a and b are moving in
  opposite directions at u m/s and v m/s, then time
  taken by the trains to cross each other (a b)
  / (u v) .
• If two trains of length a and b are moving in
  the same direction at u m/s and v m/s, then time
  taken by the faster train to cross the slower
  train (a b) / (u - v) .
• Question 2 trains of length 137 m and 163 m are
  running towards each other and speeds 42 km/hr
  and 48 km/hr respectively. In what time will the
  two trains cross each other?
• Solution
• Relative velocity 42 48 90 km/hr (90 x
  5/18) m/s 25 m/s. (Opposite directions)
• Time taken to cross each other 300 / 25 12
  sec.
• Question 2 trains running in opposite directions
  cross a man standing on the platform in 27s and
  17s respectively and they cross each other in
  23s. Find the ratio of their speeds.
• Solution
• Let the speeds be x m/s and y m/s respectively.
• Then, length of 1st train 27x and that of 2nd
  train 17y.
• Time taken to cross each other (27x 17y) / (x
  y) 23.
• 27x 17y 23x 23y.
• 4x 6y.
• x y 3 2.

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