Step 1: Standard preposition usage.
When we talk about modes of transport like train, bus, car, etc., we generally use "by."
Step 2: Apply the rule.
Correct expression: "Sumita came by train."
Step 3: Eliminate incorrect options.
(B) at – shows place, not suitable.
(C) on – incorrect here (though "on foot" is correct, "on train" is not).
(D) for – wrong usage in this context.