Problems On TrainsPage 1
1.  What is the time taken by a train running at 54 kmph to cross a man standing on a platform, the length of the train being 180 m ?  (a)10 seconds  (b)12 seconds  (c)14 seconds  (d)16 seconds 

Answer is: BSpeed of train = 54 kmph = 54 x 5/18 = 15 m/s.
Distance = length of the train = 180 m.
∴ Time = 180/15 = 12 seconds.
2.  How long will a train 100 m long and travelling at a speed of 45 kmph, take to cross a platform of length 150 m?  (a)24 seconds  (b)18 seconds  (c)20 seconds  (d)22 seconds 

Answer is: CDistance = length of the train + length of the platform.
distance = 100 + 150 = 250 m.
⇒ 45 x 5/18 = 12.5 m
∴ Time = 250/12.5 = 20 seconds.
3.  Find the length of the bridge, which a train 120 m long travelling at 54 kmph can cross in 30 seconds.  (a)330 m  (b)320 m  (c)310 m  (d)340 m 

Answer is: ASpeed of the train = 54 kmph.
⇒ 54 x 5/18 = 15 m/s
∴ distance covered in 30 seconds.
⇒ 15 x 30 = 450 m
length of bridge = distance covered – length of train.
Hence, length of bridge = 450 – 120 = 330 m
4.  Find the time taken by a train 150 m long running at a speed of 63 kmph to cross another train of length 100 m running at a speed of 45 kmph in the same direction.  (a)45 seconds  (b)60 seconds  (c)55 seconds  (d)50 seconds 

Answer is: DTotal distance covered = sum of length of the two train = 100 + 150 = 250 m
Relative speed of the two trains = 63 – 45 = 18 kmph
(since the trains are running in the same direction the relative speed will be the difference in the speeds).
⇒ 18 x 5/18 = 5 m/s
∴ Time = 250/5 = 50 seconds
5.  A train crosses two persons, cycling in the same direction as the train in 12 and 18 seconds respectively. If the speeds of the two cyclists are 9 and 18 kmph respectively, find the length and the speed of the train.  (a)90 m , 36 kmph  (b)96 m , 34 kmph  (c)94 m , 38 kmph  (d)95 m , 40 kmph 

Answer is: ALet the speed of train is s kmph
Relative speed of overtaking first cyclists = (s – 9) kmph
Time took to overtake the first cyclist = 12 seconds
∴ length of train = 12 x (s – 9) x 5/18 →(i)
Similarly, considering the case of overtaking the second cyclist,
∴ length of train = 18 x (s  18) x 5/18 →(ii)
Equating (i) and (ii),
⇒ 12 x (s – 9) x 5/18 = 18 x (s – 18) x 5/18
⇒ 2s – 18 = 3s – 54
⇒ s = 36 kmph.
Now, length = 12 x (s – 9) x 5/18 = 12 x 27 x 5/18
∴ length = 90 m
6.  How long does a train 120 m long running at the speed of 72 kmph take to cross a bridge 130 m in length?  (a)9.8 sec  (b)12.5 sec  (c)11.5 sec  (d)14.3 sec 

Answer is: BSpeed = (72 x 5/18) m/s = 20 m/s.
Total distance covered = (120 + 130) m = 250 m
∴ Required time = (250/20) sec = 12.5 sec.
7.  A train 260 m long is running at a speed of 45 kmph. In what time will it pass a bridge 240 m long?  (a)40 seconds  (b)42 seconds  (c)45 seconds  (d)48 seconds 

Answer is: ASpeed = 45 x (5/18) m/s = 25/2 m/s
Total distance covered = (260 + 240) m = 500 m
∴ Required time = 500 x (2/25) sec = 40 sec.
8.  A train running at the speed of 60 kmph crosses a pole in 18 seconds. What is the length of the train?  (a)200 m  (b)300 m  (c)324 m  (d)CBD 

Answer is: BSpeed = 60 x (5/18) m/s = (50/3) m/s.
Length of the train = (Speed x Time) = (50/3 x 18) m = 300 m.