The southern state of Kerala in India follows the Indian Standard Time. The Indian Standard Time is based on the longitude 82.5 degrees east. It is 5 hrs and 30 minutes ahead of GMT in the summer and 4 hrs 30 minutes in the winter.
When the Sun is overhead on this longitude it is exactly 12 noon in India. It would be the same in Kerala.
Most countries have their own standard time so that trade and commerce can run smoothly. Sometimes, a country may have more than one standard time, as is the case with the USA, Russia and Australia. Such countries have a vast east-west spread and require more than one standard time.
India has only one standard time.