we use e in university but why we use a in varsity

Question

we use e in university  but why we use a in varsity

Answer

They are the same word but split apart long ago. Varsity was shortened from the word university 3 centuries ago, and probably reflected the pronunciation at that time.  They are now used in different ways.

Answer

Yes, university is spelled with an "e" while varsity with an "a". They are different words having different meanings. 
varsity = the team representing a college/university in sport events 
university = institution for higher learning

Answer

What is your question? You received two perfect answers.

Answer

Then what is your question? About English orthography?

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