1. Q. A train pass a pole in 15 second and a platform 100 m long in 25 second. Find the speed of train and length of train?
Solution: Let the speed of train = x m/s Distance travel by train to cross pole = Length of train , time = 15 sec => 15x = Length of train Distance travel by train to cross platform = Length of train + Length of platform = Length of train + 100,time = 25 sec 25x = 15 x + 100 => 25x – 15x = 100 => 10x = 100 => x = 100/10 = 10m/s Length of train = 15x =15 x 10 = 150m Do yourself: A train passes an electric pole in 10 seconds and a 130 m long platform in 20 seconds. How should I calculate the length of the train? Q.2. A train 50 metres long passes a platform 100 metres long in 10 seconds. The speed of the train? Solution: Distance travel by train to cross platform = Length of train + Length of platform = 50 + 100 = 150m,,time = 10 sec Speed = d/t = 150/10= 15m/s Q.3. A train moves with a speed of 108 km/h. Find Its speed in metres per second? Solution: Speed = 108 x (1000m/3600sec) = 30m/s Q.4. In what time will a train 100 metres long cross an electric pole, if its speed be 144 km/hr? Solution: Speed = 144 x (1000m/3600sec) = 40m/s Distance travel by train to cross pole = Length of train = 100m Time =distance / time = 100/40 = 2.5sec Q.5. A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, Find the length of the train ? Solution: Time = 10min = 10 x 60 = 600sec , distance = 12km = 12000m Speed of train = 12000m/600sec = 20m/s Length of train = Distance travel by train to cross a telegraph post = speed x time = 20 x 6 = 120m Q.6. A train 110 metres long is running with a speed of 60 km/h. In what time will it pass a man who is running at 6 km/h in the direction opposite to that in which the train is going? Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr = 66 x (5/18) m/s = 55/3m/s Time taken to pass the man = Distance/speed = 110 m/ (55/3)m/s = (110x3)/55 = 6 sec Q.7.Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 km/h and 45 km/h respectively. In how much time will they cross each other, if they are running in the same direction? Solution: Relative speed of trains = (45  40) km/h = 5 km/h = 5 x(5/18 )m/s = 25/18m/s Total distance covered = Sum of lengths of trains = 200 + 150 = 350 m. Time taken = distance /speed = 350 /(25/18) = (350 x 18) /5 = 252 sec = 4 min 12sec 
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February 2020
