Thank you Bibas for your information.Yes, he is absolutely correct.Moreover I would like to comment on given below statement by Free H1B:

Also, bibas is right in pointing taking start date of OPT as end of July. That way your 60 days grace period will take you to 1st of October (which is your H1 start date). No hassel for any visa stamping, Kaplan etc.

Normally it doesn't happen in practical, there will be some gap and it is not possible to extend your OPT and grace period upto oct 1st.Be careful if you are graduating on spring.

All the best.