Explanation:

As Article 75 President is the one who constitutionally given authority in appointing the Prime Minister and other ministers. Hence they hold the office only on the pleasure of the President.
This doesn’t mean that he can remove them on his discretion, if it is so then Presidential supremecy will exist. This is perfectly balanced by Article 74 which states that President shall exercise his functions on the aid and advice of the Prime Minister and his Council of Minister.
So when the government loses the confidence or if the Prime Minister wants to step down from his duty then he will give it in writing to the President. Now President gets the authority to remove the Prime Minister.One thing has to be noted, the council of ministers who are selected by the PM will also have to step down. Thus the ship (government) will sink when the Captian (Prime Minister) jumps into the sea.