# Problems on Trains - Aptitude Questions and Answers - RejinpaulPlacement

8.
A train 100 metres long takes 6 seconds to cross a man walking at 5 kmph in a direction opposite to that of that train. Find the speed of the train.

Solution:   Let the aped of the train be x kmph. Speed of the train relative to man
= (x+5) kmph
= (x+5) * 5/18 m/sec

100/( (x+5) * 5/18) = 6
30(x+5) = 1800
x = 55

Speed of the train is 55 kmph.
9.
A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and the length of the platform.
Answer: (B) 160 m , 140 m

Solution:   Let the length of train be x metres and length of platform be y metres.

Speed of the train relative to man
= (54 – 6) kmph = 48 kmph
= (48 * 5/18) m/sec = 40/3 m/sec

In passing a man, the train covers its own length with relative speed.

Therefore, Length of train = (Relative speed * Time) = (40/3 * 12) m = 160 m.

Also, speed of the train = (54 * 5/18) m/sec = 15 m/sec.

Therefore, (x+y) / 15 = 20
x+y = 300
y = (300 – 160) m
y = 140 m
10.
A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods trainis 280 m long, find its speed.

Solution:   Relative speed
= (280/9) m/sec
= [(280/9) * (18/5)]kmph = 112 kmph.

Therefore, Speed of goods train = (112 – 50) kmph = 62 kmph
11.
A train moves with a speed of 108 kmph. Its speed in metres per second is:

Solution:   Speed of the train = 108 kmph
= (108 * 5/18) m/sec
= 30 m/sec
12.
A speed of 14 metres per second is the same as:
Solution:   Speed = 14 m/sec
= (14 * 18/5) km/hr
= 50.4 km/hr.
13.
In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr? [S.S.C 2003]

Solution:   Speed of the train
= (144 * 5/18) m/sec = 40 m/sec

Time taken = (100/40) sec = 2.5 sec.
14.
A train 280 m long, running with a speed of 63 km/hr will pass a tree in: [S.S.C. 2003]