Why StringBuffer and StringBuilder has not overridden equals() and hashCode() in java ?

Design wise, I think they shouldn't override equals nor hashcode methods since they are just builder objects. The state for these objects is just the character array from the AbstractStringBuidler. Logically, you wouldn't need to check the equality of two builder objects (someone shouldn't really care about the state of the builder) rather you need to check the equality of what is being built, which is the target String object in this case.

Because String Buffer is mutable, and its primary use is for constructing strings. If you want to compare content, call String Buffer#to String() and compare the returned value.

It is not generally useful to override hash Code() for mutable objects, since modifying such an object that is used as a key in a Hash Map could cause the stored value to be "lost."

Because it is a mutable 

Simplest reason is that because they are mutable in Java.  Understand the concept of immutability in String, you get to know automatically why these methods are not overridden.