# Problems on Trains Questions Answers

1) 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 trai

- 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}

**Ans.**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}

2) 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)

- 1) 30 Km/hr
- 2) 36 Km/hr
- 3) 80 Km/hr
- 4) 90 Km/hr

**Ans.**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

3) 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 tunne

- 1) 650 meter
- 2) 555 meter
- 3) 500 meter
- 4) 458 meter

**Ans.**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 :) ]

4) 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/

- 1) 25 Seconds
- 2) 28 Seconds
- 3) 30 Seconds
- 4) 35 Seconds

**Ans.**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}

5) 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

**Ans.**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}

6) 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 trai

- 1) 45 m
- 2) 50 m
- 3) 55 m
- 4) 60 m

**Ans.**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

7) 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

**Ans.**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}

8) 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 crossin

- 1) 10 seconds
- 2) 12 seconds
- 3) 14 seconds
- 4) 16 seconds

**Ans.**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}

9) A train is moving at a speed of 132 km/hour. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters lon

- 1) 7 second
- 2) 7.5 second
- 3) 8 second
- 4) 8.5 second

**Ans.**B

**Explanation :**

As we need to calculate answer in seconds, so first convert speed into meter/sec. we know 1 km/hr = 1*(5/18) m/sec So, Speed = 132* (5/18) = 110/3 m/sec Distance need to be covered in passing the platform = Length of train + length of platform = 110 + 165 = 275 meters Time = Distance/Speed \begin{aligned} => Time = 275* \frac{3}{110} = \frac{15}{2} \= 7.5 seconds \end{aligned}

10) In what time will a train 100 meters long cross an electric pole, if its speed is 144 km/

- 1) 5 seconds
- 2) 4.5 seconds
- 3) 3 seconds
- 4) 2.5 seconds

**Ans.**D

**Explanation :**

First convert speed into m/sec Speed = 144*(5/18) = 40 m/sec Time = Distance/speed = 100/40 = 2.5 seconds