problems on trains.35

PROBLEMS ON TRAINS

1. A train 150 m long is running at a speed of 90kmph. Time taken by

the train to cross a tree is :

Answer :6

Difficulty Level : Easy Moderately easy Difficult

Basic Formula:

Time =

Answer with Explanation:

Speed of the train = 90 kmph = 90 x = 25 m/sec.

Distance to cross the tree = Length of the train

= 150 m.

Require time = = 6 sec.

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2. A train 280m long, running with a speed of 63kmhr will pass a pole in:

Answer:12


Basic Formula:

Time :


Speed of the train = 63 km/hr = 63 x = m/secDistance to pass the pole = Length of the train

= 280 m.

Required time = = 16 sec.


3. A train is moving at speed of 132kmph. If the length of the train is

110 meters, how long will it take to cross a railway platform 165 m long?

Answer :7.5


Basic Formula:

Time :


Speed of the train = 132 kmph = 132 x = m/sDistance covered in passing the platform

= Length of the train + Length of the Platform= (110 + 165) = 275 m.

Required time = = 7.5 sec.


4. In what time will a train 100 meres long cross an electric pole, if its speed is 144 km/hr?

2.5 seconds 4.25 seconds 5 seconds 12.5 seconds


Basic Formula:

Time :


Speed of the train = 144 x = 40 m/sec.Distance covered in passing the electric pole

= Length of the train = 100 m.

Required time = = 2.5 sec.


5. 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


Basic Formula:

Time :


Speed of the train = 45 x = m/sec.Distance covered in passing the bridge

= Length of the train + Length of the bridge = 360 + 140 = 500 m

Required time = = 40 sec..


6. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:

70 km/hr 75 km/hr 84 km/hr 87.5 km/hr


Basic Formula:

Speed =


Given V1 : V2 = =

Given V2 = = 100 km/h.

= V1 = = 87.5 km/hr.


7. An express train traveled at an average speed of 100 km/hr, stopping for 3

minutes after every 75 km.. How long did it take to reach its destination 600

km from the starting point?

6 hrs 21min 6 hrs 24 min 6 hrs 27 min 6 hrs 30 min


Basic Formula:

Time :

Answer with Explanation:Speed of the train = 100 km hr.Distance = 600 km.

Time taken = = 6 hrs.

Given the train stops for 3 minutes after every 75 km.

No. of stoppings = = 8Omitting the last stopping No. of stoppings = 7Time taken at one stop = 3 min.

Time taken for 7 stops = 7 x 3 = 21 min. Total time taken to reach the destination = 6 hrs 21 min.


8. A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

230 m 240 m 260 m 270 m


Basic Formula:

Distance = Speed x Time


Length of the train = x m.Speed of the train = 72 km hr = 72 x

= 20 m/secTime taken = 26 sec.Length of the Platform = 250 m.

Total Length = (x + 250) m. (x+250) = 20 x 26 = 520

x+250 = 520

x = 270

Length of the train = 270 m.


9. A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr the time taken by it to cover the same distance will be:

10 min 11 min 20 sec 13 min 13 min 20 sec


Basic Formula:

Speed = , Time =

Answer with Explanation:Given, Distance = 10 km.Time = 12 min. = = hr.

Speed = = 50 kmphr.If the speed of the train is decreased by 5 kmphrNew Speed = 50-5 = 45 kmphr.Distance = 10 km.

Time taken = = hrs.

= x 60 = = 13.33 min. ( .33 min. = .33 x 60 sec. = 19.9 sec.)

=13 min. 20 sec.


10. 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 cm 240 cm 300 cm 110 cm


Basic Formula:



To find the length of the train : Length of the train = xSpeed of the train = 54 km/hr = 54 x = 15 m/sec.Time taken to cross the man = 20 sec.

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

To find the Length of the Platform : -

Length of the platform = ymTime taken to cross the platform = 36 sec. Total distance covered = Length the train + length of the platform

= 300 + y

300 + y = 54 x x36 =540 300 + y = 540 y = 240 m.

Length of the platform = 240 m.


11. A train 280 m long is moving at 60kmph. The time taken by the train to cross a tunnel 220 m long is: Answer: 30


Basic Formula:

Time =

Answer with Explanation:Speed of the train = 60 x = m/sec.Distance covered in passing the tunnel

= Length of the train + Length of the tunnel = 280 + 220 = 500 m.

Time taken = = 30 sec.


12. With a speed of 60kmph a train crosses a pole in 30 seconds. The length of the train is: Answer : 500


Basic Formula:



Speed of the train = 60 x = m/s.Time taken = 30 sec.

Distance = x 30 = 500 m.


13. A train traveling at a speed of 90kmph crosses a pole in 10 seconds. The length of the train is:

Answer : 250


Basic Formula:


Answer with Explanation:Speed of the train = 90 x = 25 m/sec.Time taken = 10 sec.

Distance = 25 x 10 = 250 m.


14. A train 120 m long crosses a standing man in 15 seconds. The speed of the train is: Answer: 28.8


Basic Formula:

Speed =


Distance = 120 m.Time = 15 sec. Speed = = 8 m/sec.

= 8 x = 28.8 km/hr


15. A train 700 m long is running at 72kmph. If it crosses a tunnel in I minute, the length of the length of the tunnel is: Answer: 500

Difficulty Level : Easy Moderately easy DifficultBasic Formula:



Speed of the train = 72 km/hr = 72 x = 20 m/sec.Time taken = 1 min. = 60 sec.Length of the train = 700 m.Length of the tunnel = x m

Total length = (700 + x) m. (700 + x) = 20 x 60

700 + x = 1200 x = 500

Length of the tunnel = 500 m.


16.The length of a brigade which a train 130 m long and traveling at 45kmph can cross in 30 seconds, is: Answer: 245


Basic Formula:



Speed of the train = 45 x = m/sec.Time = 30 sec.

Length of the train = 130 m.Length of the bridge= x m

Total Length = (130 + x) m (130 +x) = x 30

130 + x = 375

x =375 – 130 x = 245 m.

Length of the bridge = 245 m.


17. If a 200 m long train crosses a platform of the same length as that of the train in 20 seconds, then the speed of the train is: Answer: 72


Basic Formula:

Speed =

Answer with Explanation:Length of the train = Length of the Platform = 200 m.

Total length = 200 + 200 = 400 mTime taken = 20 sec.

Speed = = 20 m/s

= 20 x = 72 km/hr.


18. A train 60 m long passes a platform 90 m long in 10 seconds. The speed of the train is: Answer: 54


Basic Formula:

Speed =

Answer with Explanation:Length of the train = 60 m.Length of the Platform = 90 m.

Total Distance covered = 60 + 90 = 150 m.Time taken = 10 sec.

Speed = = 15 m/sec.

= 15 x = 54 km/hr.


19. A train 300 m long crossed a platform 900 m long in 1 minute 12 seconds. The speed of the train (in km/hr) is:

Answer: 60


Basic Formula:

Speed =

Answer with Explanation:Length of the train = 300 m.Length of the Platform = 900 m.Total Distance covered = 300 + 900 = 1200 m.Time taken = 1 min. 12 sec. = 72 sec.

Speed = = m/sec.

= x = 60 km/hr.


20.A train crosses a platform 100 m long in 60 seconds at a speed of 45kmph. The time by the train to cross an electric pole is: Answer: 52 sec


Basic Formula:

Distance = Speed x Time, Time =

Answer with Explanation:To find the length of the train :-

Speed of the train = 45 x = m/sec.Length of the train = x mLength of the Platform = 100 m.

Total distance covered = (x + 100) mTime = 60 sec.

100 + x = x 60 100 + x = 750 x = 650 m.


To find the time taken to cross the pole:-

Distance covered = Length of the train = 650 m. Required Time = = 52 sec.


21.A train of length 150 m long takes 40.5 seconds to cross a tunnel of length 300 m the speed of the train(in km/hr) is:Answer: 40


Basic Formula:

Speed =


Length of the train = 150 m.Length of the tunnel = 300 m.

Total Distance covered = 150 +300 = 450 m.Time taken = 40.5 sec.

Speed = x = 40 km/hr.


22.A train 150 m long takes 20 seconds to cross a platform 450 m long. The speed of the train(in m/sec) is: Answer: 30


Basic Formula:

Speed =


Length of the train = 150 m.Length of the Platform = 450 m.

Total Distance covered = 450 +150 = 600 m.Time taken = 20 sec.

Speed = = 30 m/s.


23.A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is: Answer: 150


Basic Formula:

Speed =

Answer with Explanation:To find the speed while crossing the Platform:-

Length of the train = x m.Length of the Platform = 100 m.

Total Distance covered = (100 + x) mTime taken = 25 sec.

Speed = __________________ 1

To find the speed while crossing the Pole:-

Distance covered = Length of the train = x mTime taken = 25 sec.

Speed = ________________________ 2

1 = 2 = 15 (100+x) = 25 x

x = 150 m..



24. A train takes 18 seconds to pass completely though a station162 m long and 15 seconds though another station 120 m long. The length of the train is:Answer: 90


Basic Formula:

Speed =

Answer with Explanation:To find the speed while crossing the First Station:-

Length of the train = x m.Length of the First Station = 162 m.

Total Distance covered = (x+162) mTime taken = 18 sec.

Speed = __________________ 1

To find the speed while crossing the Second Station:-Length of the Second Station = 120 m.

Total Distance covered = (x+120) mTime taken = 15 sec.

Speed = ___________________2

1 = 2 = 15 (x+162) = 18 (x+120)

x = 90 m..



25. If a train 110 m long passes a telegraph pole in 3 seconds, then the time taken by it to cross a railway platform 165 m long is: Answer: 7.5


Basic Formula:

Speed = , Time =


To find the speed of train while crossing the Pole:-

Length of the train = 110 m. Time taken = 3 sec.

Speed = m/sec.

To find the time taken while crossing the Platform:-

Length of the Platform = 165 mTotal Distance covered = 110 + 165 = 275 mSpeed of the train = m/s

Time taken = = 7.5 sec.


26. A train 110 m long is traveling at a speed of 59kmph. The time in which it will pass a passer by, walking at 4kmph in the same directions, is: Answer: 71/3


Basic Formula:Time =

Answer with Explanation:Speed of the train = 59 km/hr.Speed of the man = 4 km/hr.Since both are in the same direction Relative speed = (59-4) = 55 km/hr.Length of the train = 110

Time = =

Time = 7 sec.


27.A train 150 m long moving at a speed of 35 meters per second overtakes a man moving at 5 meters/sec in opposite direction. The train will pass the man in: Answer: 5


Basic Formula:

Time =

Answer with Explanation:Speed of the train = 35 m/sSpeed of the man = 5 m/sSince both are moving in opposite direction Relative speed = (35+5) = 40 m/sec.Length of the train = 150 m

Time = = 3.75 sec.


28.Two trains each 200 m long are running on parallel rails at the rate of 40kmph and 45kmph respectively. In how much time will they cross each other, if they are running in the same direction? Answer: 288


Basic Formula:

Time =

Answer with Explanation:Distanced covered = Total length of the two trains

= 200 + 200 = 400 m.Speed of the First train = 40 kmph.Speed of the Second train = 45 kmph.Since both the trains are moving in the same directionRelative speed = 40-45 = 05 kmph.Relative speed = 5x = m/s



29.Two trains 126 m and 114 m long are running in opposite directions, one at the rate of 30kmph and another one at 42kmph. From the moment they meet will cross each other in: Answer: 12


Basic Formula:

Time =


Distance covered = Total length of the two trains = 126 + 114 = 240 m.

Speed of the First train = 30 kmph.Speed of the Second train = 42 kmph.Relative speed = (30+42) = 72 kmph.

= 72 x = 20 m/sec.



30.A train 270 m long is moving at a speed of 24kmph. It will cross a man coming form the Opposite direction at a speed of 3kmph, in: Answer: 36


Basic Formula:

Time =


Length of the train = 270 m.Distance covered = Length of the train = 270 m.Speed of the train = 24 kmph.Speed of the man = 3 kmphSince the train and the man are moving in opposite direction Relative speed = (24+3) = 27 kmph

= 27 x = m/sec.

Required Time = = 36 sec.


31.A train 125 m long passes a man, running at 5 kmph in the same direction

in which rate train is going in 10 seconds. The speed of the trains is :

Answer : 50


Basic Formula:

Relative Speed =


Length of the train = 125 m.Time taken = 10 sec.

Speed of the train = x kmphSpeed of the man = 5 kmphSince the train and the man are moving in the same direction Relative speed = (x – 5) x m/sec.

(x -5) = x-5 = 45

x = 50 m/s.

Speed of the train = 50 m/sec.


32. A train 110 m long passes a man, running at 6 kmph in the direction

opposite tot hat of the train, in 6 secs. The speed of the train is

Answer : 60


Basic Formula:

Relative Speed =


Length of the train = 110 m

Time taken = 6 sec.

Speed of the train = x kmph

Speed of the man = 6 kmph

Since the train and the man are moving in the opposite direction

Relative speed = (x +6) x m/sec.

(x +6) x = x+6 = 66

x = 60 m/sec.

Speed of the train = 60 m/sec.


33. 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. The length of the train is :

Answer: 50


Basic Formula:

Relative speed =

Answer with Explanation: Length of the train = x m

Speed of the train = S kmph.

To find the relative speed of the train crossing the first man :-

Speed of the First man = 2 kmph., Time = 9 sec.

Relative speed = (S-2) m/sec.

(S-2) x = S = +2 ______________ 1

To find the relative speed of the train crossing the second Man:-

Speed of the second man = 4 kmph, Time = 10 sec.

Relative speed = (S-4) x m/sec.

(S-4) x = S = +4 ______________ 2

1 = 2 +2 = +4 x = 50 m. Length of the train = 50 m.


34. Two stations A and B are 110 km apart on a straight line. One train starts

from A at 7 am and towards B at 20 kmph. Another train starts from B at 8

am and travels towards A at a speed of 25 kmph. At what time will they

meet?

Answer : 10 am


Basic Formula:



Suppose the two trains meet x hrs after 7 am

Distance covered by A in x hrs = 20 x x km.

Distance covered by B in (x-1) hrs = 25 (x-1) km.

Given distance between the two stations = 110 km.

20 x + 25 (x-1) = 110

45 x = 135

x = 3 hrs.

The two trains meet at 10 am.


problems on trains.35

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