Arithmatical - Problems on Trains

DIRECTIONS : Problems based on Trains.
6. A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
  A.  10 sec.
  B.  12 sec.
  C.  14 sec.
  D.  16 sec.
Solution
Speed of the train = (59 + 7) Kmph
= (66 x 5/18) m/sec
= (55 / 3 )m/sec
Time taken by it cover 220 m = (220 x 3 /55)sec
= 12 sec
7. 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
Solution
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
8. A train 108 m long moving at a speed of 50 km / hr crosses a train 112 m long coming from opposite direction in 6 seconds. The speed of the second train is
  A.  48km/hr
  B.  54 km/hr
  C.  66km/hr
  D.  82km/hr
Solution
Relative speed = (x + 50) km/ hr
=(x + 50) x 5/18 m/sec
= 250 + 5 x /18]m/sec
Distance covered = (108 + 112) m
= 220 m
= 220 / (250 + 5x / 18) = 6
= 250 + 5 x= 660
= 82 km/hr.
9. How long does a train 110 metres long running at the speed of 72 km / hr take to cross a bridge 132 metres in length?
  A.  9.8 sec
  B.  12.1 sec
  C.  12.42 sec
  D.  14.3 sec
Solution
Speed = (72 x 5/18 )m/sec
= 20 m/ sec
Total Distance covered = (110 + 132) m
= 242 m
Required time = (242 / 60) sec
= 12.1 sec
10. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr?
  A.  2.5 sec
  B.  4.25 Sec
  C.  5 sec
  D.  12.5 sec
Solution
Speed = (144 x 5 /18) m/sec
= 40 m / sec
Time taken = (100 /40) sec
= 2.5 sec.
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