Question

how was the conflict between the central government and state government resolved

Answer 1

it was resolved by the means of federalism ie the form of power sharing where power is shared between two or three levels of govt

Answer 2

If there is a conflict between the central government and state government,

The Supreme Court, according to Forty-second Amendment Act, 1976, has given the exclusive jurisdiction in controversies concerning the distribution of legislative powers.  

However, there may be situations, which may need that such problems should not suffer a long drawn process of lawsuit and the Supreme Court should be allowed to dispose of such queries lastly and rapidly.