Problems On Trains Aptitude Questions and Answers
This section focuses on "Problems on Trains" of Quantitative Aptitude. These Multiple Choice Questions (mcq) should be practiced to improve the Quantitative Aptitude skills required for various interviews (campus interviews, walk-in interviews, company interviews), placements, entrance exams and other competitive examinations.
1. A train running at the speed of 72 km/hr crosses a man standing on the platform in 12 seconds. What is the length of the train?
Explanation: Speed = (72*5)/18=20m/s
Length of the train = (Speed x Time).
Length of the train = 20*12=240m
2. A train 100 m long passes a boy, running at 3 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
Explanation: Speed of the train relative to boy = 100/10 = 10m/s
(10*18)/5 = 36 km/hr.
Let the speed of the train be x km/hr.
Then, relative speed = (x - 3) km/hr => x - 3 = 36 => x = 39 km/hr
3. A train 100 metres long and travelling at 54 km/hr can cross the bridge in 20 seconds, What will be length of the bridge?
Explanation: Speed = (54*5)/18=> 15m/sec
Time = 20 sec.
Let the length of bridge be x metres.
Then, (100 + x)/20 = 15
100 + x = 300
x = 200 m.
4. A train 300 m long is running at a speed of 36 km/hr. In what time will it pass a bridge 120 m long?
Explanation: Speed = (36*5)/18= 10m/s
Total distance to be covered = (300 + 120) m = 420 m.
Formula for finding Time = Distance/Speed
Required time = 420/10=>42 sec.
5. A train 210 m long passes a man standing in 21 seconds. How long will it take to pass a bridge of 500 m long?
Explanation: Speed = 210/21 => 10m/s
Required time = (210+500)/10 => 71 sec
6. A train 125 metres long is running with a speed of 45 kmph. In what time will it pass a car who is running at 30 kmph in the direction opposite to that in which the train is going?
Explanation: Speed of train relative to car = (60 + 30) km/hr = 90 km/hr.
(90*5)/18 => 25m/s
Time taken to pass the car = 125/25 => 5 Sec
7. Two trains 100 m and 150 m long run at the speed of 36 km/hr and 54 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:
Explanation: Relative speed = (36 + 54) km/hr = 90 km => 25 m/s
Distance covered in crossing each other = (100 + 150) m = 250 m.
Required time = 250 x 25 sec = 10 sec.
8. A train speeds past a pole in 10 seconds and a bridge of 100 m long in 20 seconds. Its length is
Explanation: Let the length of the train be x metres and its speed by y m/sec.
Then, x/y = 10 => y = x/10
Therefore (x + 100)/20 = x/10
=> 10(x + 100) = 20x
=> 10x + 1000 = 20x
=> 1000 = 10x
=> x = 100 m.
9. How many seconds will a 500 metre long train take to cross a man walking with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 66 km/hr?
Explanation: Speed of the train relative to man = (63 - 3) km/hr = 60 km/hr => 50/3 m/s
Time taken to pass the man = (500*3)/50 => 30sec.
10. Two stations A and B are 220 km apart on a straight line. One train starts from A at 8 a.m. and travels towards B at 40 kmph. Another train starts from B at 9 a.m. and travels towards A at a speed of 50 kmph. At what time will they meet?
Explanation: Suppose they meet x hours after 8 a.m.
Distance covered by A in x hours = 40x km.
Distance covered by B in (x - 1) hours = 50(x - 1) km.
40x + 50(x - 1) = 220 => 90x = 270 => x = 3
So, they meet at 11 a.m.
11. Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Explanation: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = root(b) : root(a) = root(16) : root(9) = 4 : 3.
12. A shatabadi express takes 240 seconds to cover a distance of length 700 meters at a speed of 270 km/hr.
What will be the time taken by the train to cross a standing pole?
Explanation: Speed of the train = 270 km/hr => 75m/s.
distance/speed = time
x+700/75 = 240 => x+700 = 18000 => x = 17300 m
The time taken by the train of length 17300 meters to cross a standing Pole at 75 m/s =( 17300/75)seconds
= 231 seconds
13. A train 135m long is moving at a speed of 12.5 km/h. It will cross a girl coming from the opposite direction
at a speed of 1km/hr in.
Explanation: Relative speed = speed of train + speed of girl => (12.5 + 1) km/hr => 13.5 km/hr => 3.75 m/s
Time = distance / speed
Time taken by the train to pass the man = 135 / 3.75
= 36 sec.
14. A boy sitting in a train which is travelling at 25 km/hr observes that a goods train travelling in opposite
direction, takes 4.5 seconds to pass him. If the train is 140 m long, find its speed.
Explanation: Relative speed = distance / time
= (140 / 4.5) m/s => 31.11 m/s => 112 km/hr
speed of train = Relative speed - speed of train (by sitting) => (112 – 25) km/hr => 87 km/hr
15. The Mumbai express 500m long passes a man running at 20km/hr in the same direction in which the
express is going in 40sec. The speed of the express is.
Explanation: Length of the train = 500m
Speed of the expess relative to man = (500 / 40)m/s => 25/2 m/s => 45km/hr
Let the speed of the express be 'x' km/hr
Then the relative speed = (x -20)km/hr
Therefore x – 20 = 45 => x = 45 + 20 => 65km/hr
16. A girl is walking at a speed of 15 km/hr along a railway track. If she is 600 m ahead of the train which is
300 m long and runs at a speed of 180 km/hr in same direction, then what is the time required to pass a girl?
Explanation: Speed of train relative to walking person (girl) = (180 -15)kmph= 165 kmph => 45.83 m/s
Distance to be covered by the train = (600+300)m = 900m
Therefore, time taken by the train to cross the girl = Distance over speed => 900 /45.83 => 19.63
17. Two trains A and B are moving in opposite directions at 180 km/hr and 270 km/hr. their lengths are 3.30
km and 2.7 km respectively. The time taken by the slower train to cross the faster train in second is.
Explanation: Relative speed = (180 + 270)km/hr => 450 km/hr => 125m/s
Distance covered = (3.30 + 2.70)km => 6000m
Required time = 6000 / 125 => 48sec
18. Two trains 300 metres and 360 metres long are running in the same direction with speeds of 216 kmph
and 162 kmph .In how much time will the first train cross the second?
Explanation: Relative speed =(216-162)kmph => 54kmph => 15 m/s
Time taken by the trains to cross each other=Time taken to cover (300+360)m at 15 m/s => (660/15) sec => 44 sec
19. A train M speeding with 60km/hr crooses another train N, running in the same direction in 1 min. If the
lengths of the trains M and N be 50m and 100m respectively. What is the speed of train N?
Explanation: Let the speed of be train N be 'x' km/hr
Speed of M relative to N = (60 – x)km/hr
=> (60-x) * (5/18)m/s
=> (300 – 5x / 18)m/s 150 / (300 – 5x / 18) =60 =>
x= 153/3 => x=51km/hr.
20. Find the time taken by mailtrain 200m long running at a speed of 120 km/hr to cross another train of
length 160m running at a speed of 96km/hr in the same direction.
Explanation: Total distance covered to cross each other = 200 + 160 = 360m
Relative speed of two trains (same direction) = (120 – 96)km/hr => 24 km/hr => (20/3)m/s
Time taken to cross = distance / speed => 360 / (20/3) => 54sec