The FR’s and DPSP are enshrined in part III and Part IV of the constitution. The former is justiciable and latter is not. In order to implement DPSP the FR’s gets violated. The conflict arises when the State needs to implement a directive principle and it infringes/ abridges the fundamental rights of the citizens.
Earlier judgements gave primacy to Fundamental rights but latter with the amendments this equations was made reversible. In the Minerva Mills v/s Union of India (1980) case, The SC held that there is harmonious relations between FR and DPSP. Both are complimentary to each other and giving supremacy to one will jeopardise the harmony. The supreme court to the view that there is no conflict between the Fundamental Rights and the DPSP and they were complimentary of each other. There was no need to sacrifice one for the sake of the other. If there is a conflict it should be avoided as far as possible.