## Arithmatical - Problems on Trains

DIRECTIONS : Problems based on Trains.
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.
Solution
 Speed of the train = (30 x 5/18)m/sec = (25 / 3) m/sec. = 100 m. = 100 /( 25 / 3) =(100 x 3 / 25) sec = 12 sec.
2. 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 train is 280 m long, find its speed? A.  52 kmph. B.  62 kmph. C.  72 kmph. D.  80 kmph.
Solution
 Relative Speed = (280 / 9)m/sec = (280/9 x 18/5) = 112 kmph. = (112 - 50)kmph = 62 kmph.

3. A train 150 m long is running with a apecd of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going? A.  6 sec. B.  7 sec. C.  9 sec. D.  11 sec.
Solution
Speed of the train relative to man =( 68 - 8 ) = 60 Kmph = 60 x 5 / 18 =50/3 m/sec. = (112 - 50)kmph = (150 x 3/50)sec = 9 sec.
4. A train moves with a speed of 108 kmph. Its speed in metres per second is A.  10.8 B.  18 C.  30 D.  38.8
Solution
 Speed = 108 Kmph = (108 x 5/18)m/sec = 30 m/sec.
5. 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
Solution
 Relative Speed = (36 + 45) km/hr = (81 x 5/18) m/sec = (45/2) m/sec = (45 / 2 x 8) m = 180 m.
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