According to grumios story that he tell curtis at the beginning of act 4 why did petruchio beat him on he way home ?

Patrichio beat Curtis for trivial reasons while on his way to home.

Explanation:

The Taming of the shrew is a comedy play written by William Shakespeare. Katherine, Patrichio, Bianca, Baptista, and Lucentio are some of the main character of the play.  

Curtis is one of many servant of Patruchio. Curtis and Grumio (servants) was having a normal conversation about their master and his wife who were about to arrive. And as soon as Patruchio arrives he starts behaving in a very aggressive and odd manner. Anthers he starts beating his servant Curtis without any significant reason.

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