What is the difference between the following interrogative structures?
What train are you going on/by?
Which train are you going on/by?
And which of the prepositions, given at the end of both structures, would be appropriate?
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Practically speaking, they both mean the same thing. Perhaps if there were a number of trains at a station, someone would say "which" train, but "what" is also acceptable.
In terms of the preposition, I have heard both prepositions used.
Personally, I would say either "Which train are you taking?" or "Which train are you on?"