Problems on Trains Questions Answers

• 8. Speed of a goods train is 72 km/hr. This train crosses a 250 meter platform in 26 seconds. Then find the length of goods train.

  1. 250 meters
  2. 260 meters
  3. 270 meters
  4. 280 meters

  Answer And Explanation

  Answer: Option C

  Explanation:

  First convert speed from km/hr to m/sec
  
  So, Speed = 72*(5/18) = 20 m/sec
  Time = 26 seconds
  
  Let the length of the train be x meters.
  We know, Distance = Speed*Time.
  [you can remember this formula as remembering DUST = D*ST... Distance=Speed*Time]
  
  x+250 = 20*26
  => x = 270 meters
  
  So length of the goods train is 270 meter

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• 9. A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.

  1. 310 meter
  2. 335 meter
  3. 345 meter
  4. 350 meter

  Answer And Explanation

  Answer: Option D

  Explanation:

  Speed = Distance/time = 300/18 = 50/3 m/sec
  
  Let the length of the platform be x meters
  then
  \begin{aligned}
  Distance = Speed*Time \\
  x+300 = \frac{50}{3}*39 \\
  =>3(x+300)= 1950 \\
  => x = 350 \text{ meters}
  \end{aligned}

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• 10. A train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds. What is length of the train ?

  1. 140 meter
  2. 145 meter
  3. 150 meter
  4. 155 meter

  Answer And Explanation

  Answer: Option C

  Explanation:

  Let the length of the train is x meter and Speed of the train is y meter/second
  Then x/y = 15 [because distance/speed = time]
  => y = 15/x
  
  \begin{aligned}
  => \frac{x+100}{25} = \frac{x}{15} \\
  x = 150 \text{ meters}
  \end{aligned}
  
  So length of the train is 150 meters

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• 11. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?

  1. 1:3
  2. 3:2
  3. 3:5
  4. 3:7

  Answer And Explanation

  Answer: Option B

  Explanation:

  Let the speeds of the two trains be x m/sec and y m/sec respectively.
  
  Then, length of the first train = 27x metres,
  Length of the second train = 17y metres.
  [because distance = speed*time]
  
  \begin{aligned}
  \frac{27x+17y}{x+y} = 23 \\
  => 27x + 17y = 23x + 23y \\
  => 4x = 6y \\
  => \frac{x}{y} = \frac{6}{4}
  \end{aligned}
  So ratio of the speeds of train is 3:2

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• 12. Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is ?

  1. 40 meter
  2. 45 meter
  3. 50 meter
  4. 55 meter

  Answer And Explanation

  Answer: Option C

  Explanation:

  Let the length of each train is x meter
  Distance will be x+x = 2x
  
  Relative Speed = 46-36 = 10 km/hr
  = 10*(5/18) = 25/9 m/sec
  
  Distance = Speed*Time
  
  \begin{aligned}
  2x = \frac{25}{9}*36 \\
  2x = 100 \\
  => x = 50
  \end{aligned}
  So length of both the trains are 50 meters

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• 13. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

  1. 220 meter
  2. 225 meter
  3. 230 meter
  4. 235 meter

  Answer And Explanation

  Answer: Option C

  Explanation:

  As trains are running in opposite directions so their relative speed will get added
  So, Relative speed = 120 +80 = 200 kmph
  = 200*(5/18) = 500/9 m/sec
  
  Let the length of other train is x meter then
  
  \begin{aligned}
  \frac{x+270}{9} = \frac{500}{9} \\
  => x+270 = 500\\
  => x = 230
  \end{aligned}
  
  So the length of the train is 230 meters

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• 14. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other, is

  1. 9.8 seconds
  2. 10.8 seconds
  3. 11.8 seconds
  4. 12.8 seconds

  Answer And Explanation

  Answer: Option B

  Explanation:

  Relative Speed = 60+40 = 100 kmph
  = 100*(5/18) = 250/9 m/sec
  
  Distance = 140+160 = 300 meters
  
  Time = Distance/Speed
  
  \begin{aligned}
  300*\frac{9}{250} = \frac{54}{5} \\
  = 10.8 \text{ seconds}
  \end{aligned}
  
  So the time trains will take to cross each other will be 10.8 seconds

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