Problems on Trains Questions Answers

• 15. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 seconds. What is the length of the fast train ?

  1. \begin{aligned} 27\frac{7}{9} \end{aligned}
  2. \begin{aligned} 28\frac{7}{9} \end{aligned}
  3. \begin{aligned} 29\frac{7}{9} \end{aligned}
  4. \begin{aligned} 30\frac{7}{9} \end{aligned}

  Answer And Explanation

  Answer: Option A

  Explanation:

  As Trains are moving in same direction,
  So, Relative Speed = 40-20 = 20 kmph
  = 20*(5/18) = 50/9 m/sec
  
  Length of Train= Speed * Time
  
  \begin{aligned}
  Length = \frac{50}{9}*5 \\
  = \frac{250}{9} \\
  =27\frac{7}{9}
  \end{aligned}

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• 16. Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is

  1. 30 Km/hr
  2. 36 Km/hr
  3. 80 Km/hr
  4. 90 Km/hr

  Answer And Explanation

  Answer: Option B

  Explanation:

  Distance covered = 120+120 = 240 m
  Time = 12 s
  
  Let the speed of each train = x.
  Then relative velocity = x+x = 2x
  
  2x = distance/time = 240/12 = 20 m/s
  
  Speed of each train = x = 20/2 = 10 m/s
  
  = 10*18/5 km/hr = 36 km/hr

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• 17. A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel ?

  1. 650 meter
  2. 555 meter
  3. 500 meter
  4. 458 meter

  Answer And Explanation

  Answer: Option C

  Explanation:

  Let length of tunnel is x meter
  Distance = 800+x meter
  Time = 1 minute = 60 seconds
  
  Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
  
  Distance = Speed*Time
  \begin{aligned}
  => 800+x = \frac{65}{3}*60 \\
  => 800+x = 20*65 = 1300 \\
  => x = 1300 - 800 = 500 \\
  \end{aligned}
  
  So the length of the tunnel is 500 meters.
  
  [If you want to calculate it practically, then please have your copy and pen and take a ride of Kalka to Shimla toy train in north India. It has many tunnels on the way :) ]

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• 18. How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr

  1. 25 Seconds
  2. 28 Seconds
  3. 30 Seconds
  4. 35 Seconds

  Answer And Explanation

  Answer: Option C

  Explanation:

  Relative Speed = 63-3 = 60 Km/hr
  = 60 *(5/18) = 50/3 m/sec
  
  Time taken to pass the man will ne
  \begin{aligned}
  500*\frac{3}{50} = 30 \text{ seconds}
  \end{aligned}

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• 19. A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger ?

  1. 30 seconds
  2. 32 seconds
  3. 34 seconds
  4. 36 seconds

  Answer And Explanation

  Answer: Option D

  Explanation:

  Speed of train relative to jogger = (45-9) = 36 kmph
  = 36*(5/18) = 10 m/sec
  
  Distance to cover = 240 + 120 = 360 metres
  
  Time = Distance/Speed
  So,
  \begin{align}
  Time = \frac{360}{10} = 36 \text{ Seconds}
  \end{align}

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• 20. Two trains 140 metre and 160 metre long run at the speed of 60 km/hr and 40 km/hr respectively in opposite direction on parallel tracks. What time these will take to cross each other ?

  1. 10.7 Seconds
  2. 10.8 Seconds
  3. 10.9 Seconds
  4. 11.8 Seconds

  Answer And Explanation

  Answer: Option B

  Explanation:

  Relative Speed = 60+40 = 100 Kmph
  = 100*(5/18) = 250/9 m/sec
  
  Distance to be covered = 140 + 160 = 300 metres
  
  Time = Distance/Speed
  
  \begin{aligned}
  Time = 300*\frac{9}{250} \\
  = \frac{54}{5} = 10.8\text{ seconds}
  \end{aligned}

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• 21. A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. Find the length of train ?

  1. 45 m
  2. 50 m
  3. 55 m
  4. 60 m

  Answer And Explanation

  Answer: Option B

  Explanation:

  First person speed = 2*(5/18) = 5/9 m/sec
  Second person speed = 4*(5/18) = 10/9 m/sec
  
  Let the length of train is x metre and speed is y m/sec
  
  then,
  \begin{aligned}
  \frac{x}{y-\frac{5}{9}} = 9 \\
  => 9y-5 = x \\
  => 9y-x = 5 .....(i) \\
  Also, \\
  \frac{x}{y-\frac{10}{9}} = 10 \\
  90y-9x = 100 .....(ii)\\
  
  \text{from (i) and (ii), we get,} \\
  x=50
  \end{aligned}
  So length of train is 50 metre

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