Trains Problems Questions Answers

• 8. 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 :

  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 :) ]

• 9. 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 :

  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

• 10. 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 :

  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}

• 11. A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length.

  1. 20 seconds
  2. 30 seconds
  3. 40 seconds
  4. 50 seconds

  Answer :

  Option C

  Explanation:

  Speed = 45 Km/hr = 45*(5/18) m/sec
  = 25/2 m/sec
  Total distance = 360+140 = 500 meter
  
  Time = Distance/speed
  \begin{aligned}
  = 500*\frac{2}{25} = 40 seconds
  \end{aligned}

• 12. A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

  1. 10 seconds
  2. 12 seconds
  3. 14 seconds
  4. 16 seconds

  Answer :

  Option B

  Explanation:

  As we need to get answer in seconds, so never forget to convert speed into meter per second.
  
  Speed = 30 km/hr = 30* 5/18 m/sec
  = 25/3 m/sec
  
  Distance = length of train = 100 meter
  
  Required time =
  \begin{aligned}
  \frac{Distance}{Speed} \\
  = \frac{100}{\frac{25}{3}} \\
  = 100* \frac{3}{25} = 12 sec \\
  \end{aligned}

• 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 :

  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

• 14. 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 :

  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