Quantitative Aptitude Questions and Answers - Problem on Trains
11. 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
12. 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.
13. 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
14. 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.
15. 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.
16. 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
17. 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
18. 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
19. 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
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