Arithmatical - Problems on Trains

DIRECTIONS : Problems based on Trains.
30. How many seconds will a 500 metre long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
  A.  25
  B.  30
  C.  40
  D.  45
Solution
Speed of train relatively to man = ( 63 - 3)km/hr
= 60 km /hr
= (60 x 5 / 18)m/sec
= (50 /3) m/sec
Time taken to pass the man = (500 x 3 / 50)sec
= 30 sec.
31. Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
  A.  72 sec
  B.  132 sec
  C.  192 sec
  D.  252 sec
Solution
Relative Speed= (45 - 40 ) Kmph
= 5 kmph
=(5 x 5 / 18)m/sec
= (25 / 18 ) m/sec
Time taken= (350 x 18 / 25) sec
= 252 sec.

32. 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
Solution
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.
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