Train Aptitude Solved Problems and Answers

1. A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line.
A.   10 sec.   
B.   12 sec.
C.   14 sec.   
D.   16 sec.

Explanation:

Speed of the train = (30 x 5/18)m/sec
                            = (25 / 3) m/sec.
Distance moved in passing the standing man = 100 m.
Required time taken = 100 /( 25 / 3)
                               = (100 x 3 / 25) sec
                               = 12 sec.

2. A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.
A.   52 kmph.   
B.   62 kmph.
C.   72 kmph.   
D.   80 kmph.

Explanation:

Relative Speed    = (280 / 9)m/sec
                           = (280/9 x 18/5)
                           = 112 kmph.
Speed of the train = (112 - 50)kmph
                            = 62 kmph.

3. Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ?
A.  9 a.m   
B.  10 a.m
C.  10-30 a.m   
D.  11 a.m

Explanation:

Distance covered by A in x hours    = 20 x km
Distance covered by B in (x - 1) hours    = 25 (x - 1) km
                                                              = 20x + 25 (x - I)
                                                              = 110
                                    => 45x = 135
                                              x = 3.
  So, they meet at 10 a.m

4. Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 8 seconds. The length of the faster train is
A.   80 m   
B.   100 m
C.   120 m   
D.   180 m

Explanation:

Relative speed    = (36 + 45) km/hr
                          = (81 x 5/18) m/sec
                          = (45 / 2) m/sec
Length of the train    = (45 / 2 x 8) m
                               = 180 m.

5. 30. A train 110 m long passes a man, running at 6 kmph in the direction opposite to that of the train, in 6 seconds The speed of the train is
A.  54 km/hr   
B.  60 km/hr
C.  66 km/hr   
D.  72 km/hr

Explanation:

Speed of the train relative to man    = (110 / 6 ) m/sec
                                                      = (110 / 6 x 18 /5) km/hr
                                                      = 66 km/hr
speed of the train be x kmph.
Relative Speed    = (x + 6 ) kmph.
                           = x + 6
                           = 66
x = 60.