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Let us assume the length of the train is L m.
The train passes a pole in 10 seconds and a bridge of length 2 kilometers in 110 seconds.
The speed of the from the fact that it crosses a pole in 10 sec is L/10 m/sec.
When the train crosses the bridge it has to travel a distance equal to the sum of its length and that of the bridge.
This gives the speed of the train as (L + 2000)/110 m/sec
As the two speeds are equal L/10 = (L + 2000)/110
=> 11L = L + 2000
=> 10L = 2000
=> L = 200
The length of the train is 200 m.
Its speed is 20 m/sec.
While train is passing pole
Let length of train =x
Length of pole is negligible
=> Total distance=x
Time = 10 secs
=> Speed = Distance/Time= x/10 m/s
While train is passing station
Total distance = x + 2000 metre
Time = 110 sec
Speed = (x + 2000)/110
Assuming the speed of train to be constant
=> x/10 = (x+2000)/110
=> 11x = x+2000
=> 11x -x = 2000
=> x = 2000/10 = 200 metres
=> Speed = x/10 = 200/10
=> Speed = 20 m/s
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