Hi Kumar,
the start and stop timeout are related to the following issues:
Start: upon start-up, MySQL may have to perform InnoDB recovery. If you have very large Innodb log files, that may take a long time and you may need a bigger start timeout. Another reason why it could take a long time to start is when a database has many 100k tables.
Stop: Stop is also related to the InnoDB log file size. If you have a server with a lot of memory, slow storage and large innodb log files, when MySQL stops it may have to flush a large number of dirty InnoDB pages. Again, the default stop values (either 60s or 120s) may not be sufficient.
I most cases, MySQL starts and stops in a few seconds so 60s is way sufficient.