Breakdown:
* আজ (Aj): Today
* দুপুরে (dupore): At lunchtime
* তুমি (tumi): You
* কী (ki): What
* খেয়েছিলে (kheyechehile): Did eat (past tense of "kheye")
This sentence uses the formal "tumi" which is respectful. You could also use the informal "tui" to make it less formal, but it's generally best to use "tumi" unless you know the person very well.