If the train passes the pole in 5 seconds, and the train is 50 meters long, its speed is 10 meters per second. You can find that by dividing its length by the time that it takes to pass a given point.
From the time that the front of the train reaches the bridge, it will take 50 seconds (500 meters divided by 10 meters per second) for the front to cross the bridge. However, the rest of the train will still be on the bridge.
It will be 5 more seconds (50 meter train divided by 10 meters per second) for the rest of the train to get off the bridge.
Therefore, from the time that the front of the train reaches the bridge, it will be 55 seconds until the end of the train gets off the bridge on the other side.
The train is 50m in length and crosses a pole in 5 seconds. Therefore its speed which is given by distance/ time is 50/5 or 10 m/s.
Now if the train has to cross the bridge which is 500m long make sure of not assuming that the total distance to be travelled is 500m. As the length of the train is 50m, only when the front end of the train moves 50m ahead after crossing the bridge will the rear end also cross the bridge. Therefore the total distance that has to be travelled is 550m.
As time is given by distance/speed it is 550/10=55s.
The length of the train = 50m.
To pass the pole the entire length of 50 meter the train has to pass the pole for which time taken = 5 secs.
Therefore train has moved 50 m in 5 seconds. So the speed of the train = 50m/5 sec = 10meter per sec = 50m*60*60 per hour = 180000m/s = 180 km/hour.
To cross the bridge of 500 m the train has to move over from one end to the other end of the bridge and the train has to clear its length. So the train has to move by bridge length+it's(train's) length = 500m+50m = 550m
So the time taken by train to pass the bridge = 550m/speed of train = 550m/10m/s = 55seconds.