state and central GST

yes because you service provide with in state , so you have to charge SGST and CGST fifty fifty percent.

It's equal tax management.
when a person is selling an item or providing a service in a state should pay the tax equally to both the state and center (CGST & SGST in intra state)& if the person is selling or providing the service in another state then the tax will directly go to centre (IGST in Inter State).

Intra State can be divided equally between state and centre (2 parties) but Inter State cannot be divided between 2 states and centre (3 parties) and it'll a burden on every citizen.