# Problems on Trains

## Problems on Trains

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 Question 1
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
 A 120 metres B 180 metres C 324 metres D 150 metres
Question 1 Explanation:
Speed= (60 x5/18)m/sec =50/3 m/sec. Length of the train = (Speed x Time). Length of the train =(50/3)x 9 m = 150 m.
 Question 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:
 A 45 km/hr B 50 km/hr C 54 km/hr D 55 km/hr
Question 2 Explanation:
Speed of the train relative to man =(125/10) m/sec =(25/2)m/sec. =((25/2)x(18/5)km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 x = 50 km/hr.
 Question 3
The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
 A 200 m B 225 m C 245 m D 250 m
Question 3 Explanation:
Speed = 45 x(5/18)m/sec =25/2 m/sec. Time = 30 sec. Let the length of bridge be x metres. Then, (130 + x)/30=25/2 => 2(130 + x) = 750 =>x = 245 m.
 Question 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 ..
 A 1 : 3 B 3 : 2 C 3 : 4 D None of these
Question 4 Explanation:
Let the speeds of the two trains be x m/sec and y m/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
 Question 5
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform ?
 A 120 m B 240 m C 300 m D None of these
Question 5 Explanation:
Speed = 54 x(5/18)m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x metres. Then, (x + 300)/30= 15 ==>x + 300 = 540 ==>x = 240 m.
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