Problems on Train

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

• 120 metres

• 180 metres

• 324 metres

• 150 metres

Answer explanation

Speed

=(60 x5/18)m/sec

=(50/3)m/sec.

Length of the train = (Speed x Time).

Length of the train =(50/3 x 9)m = 150 m

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

• 45 km/hr

• 50 km/hr

• 54 km/hr

• 55 km/hr

Answer explanation

Speed of the train relative to man

= (125/10)m/sec

=(25/2)m/sec

= 45 km/hr.

Let the speed of the train be x km/hr.

Then, relative speed = (x - 5) km/hr.

x - 5 = 45     -->   x = 50 km/hr.

The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

• 200 m

• 225 m

• 245 m

• 250 m

Answer explanation

Speed

=(45 x5/18)m/sec

=(25/2)m/sec.

Time = 30 sec.

Let the length of bridge be x metres.

Then,

(130 + x)/ 30 =25/2

=> 2(130 + x) = 750

=> x = 245 m.

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 : 3

• 3 : 2

• 3 : 4

• None of these

Answer 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,

and length of the second train = 17y metres.

(27x + 17y)/(x+ y) = 23

=>27x + 17y = 23x + 23y

=>4x = 6y

=>x/y=3/2

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

• 120 m

• 240 m

• 300 m

• None of these

Answer explanation

Speed

=(54 x5/18)m/sec

= 15 m/sec

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then,

(x + 300)/36 = 15

=> x + 300 = 540

=> x = 240 m

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

• 65 sec

• 89 sec

• 100 sec

• 150 sec

Answer explanation

Speed

=(240/24)m/sec

= 10 m/sec

Required time

=(240 + 650)/10sec

= 89 sec

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:

• 50 m

• 72 m

• 80 m

• 82 m

Answer explanation

Let the length of each train be x metres.

Then, distance covered = 2x metres.

Relative speed

= (46 - 36) km/hr

=(10 x5/18)m/sec

=(25/9)m/sec

2x/ 36 =25/9

=>2x = 100

=>x = 50

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

• 40 sec

• 42 sec

• 45 sec

• 48 sec

Answer explanation

Formula for converting from km/hr to m/s:  

X km/hr = ( X * 5/18)m/s.

Therefore, Speed

=(45 x5/18)m/sec

=25/2m/sec

Total distance to be covered = (360 + 140) m = 500 m.

Formula for finding Time =Distance/Speed

Required time

=(500 x 2)/25 sec

= 40 sec

Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

• 36

• 45

• 48

• 49

Answer explanation

Relative speed = (60+ 90) km/hr

   =(150 x5/18)m/sec

   =(125/3)m/sec

Distance covered

= (1.10 + 0.9) km

= 2 km

= 2000 m.

Required time

=(2000 x3/125)sec

= 48 sec.

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

• 3.6 sec

• 18 sec

• 36 sec

• 72 sec

Answer explanation

Speed of train relative to jogger

= (45 - 9) km/hr

= 36 km/hr

=(36 x5/18) m/sec

= 10 m/sec.

Distance to be covered

= (240 + 120) m

= 360 m

Time taken

=(360/10) sec

= 36 sec