Here's how I see it:
the train is X meters long. At the speed it is traveling it will run it's entire length of X meters in 35 seconds. It takes 55 seconds for it to go 300+X meters (the 300 meters of the platform plus the length of the train to get the tail end past the platform).
So it goes 300 meters in 20 seconds (55-35) and X meters in the other 35.
the train is 525 meters long
perhaps my understanding of the problem is off, but that's my answer for better or worse