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#1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

Solution:
Speed=(60×5/18)m/sec=(503)m/sec
Length of the train = (Speed×Time)
Length of the train = (50/3×9)m=150m

#2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

Solution:
Speed of the train relative to man=(125/10)m/sec
=(25/2)m/sec
=(25/2×18/5)km/hr
=45km/hr
Let the speed of the train be xkm/hr.
Then, relative speed=(x5)km/hr
x5=45x=50km/hr

#3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

Solution:
Speed=(45×5/18)m/sec=(252)m/sec
Time=30sec Let the length of bridge be x metres
Then,130 x/30=25/2
2(130 x)=750
x=245m

#4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

Solution:
Let the speeds of the two trains be x m/sec and ym/sec respectively.
Then, length of the first train=27x metres,
and length of the second train=17y metres.
27x 17y/x y=23
27x 17y=23x 23y
4x=6y
x/y=3/2