Question

if every states follow its local time what problems do arise

Answer 1

If every state start to follow its own local time it will be full of utter confusion.
the timings of the arrival of trains,flights,timings of TV programs may also bring us confusion.
For eg: one TV program starts at 7:00pm in Delhi it may start at 7:30(just an assumption )at Mumbai,whereas the adds will be giving one particular time for one program which may be telecast-ed at different timings at different places.So things like this may be confused so one country follows only one time which iss called standard time of that country.