How did the Hindus and Muslims of the Indian subcontinent address their differences after gaining independence from the British?

The subcontinent was divided into separate countries by religion.

India was formed from the areas where the majority of the population was Hindu.

Pakistan (and West Pakistan, later Bangladesh) was designated as a Muslim nation, and many Muslims from India relocated there. Some were compelled by violence to do so. Concurrently, many Hindus who lived in Pakistan also fled across the border to the new Indian nation.

The independence of the region was acknowledged by the Indian Independence Act of 1947, ending British rule of the region. Areas where the majority of residents were considered Muslims were incorporated into East and West Pakistan, separated completely by the intervening Hindu majority areas (India). In 1971, West Pakistan gained independence as Bangladesh.

Conflicts and territorial disputes continued into the 21st Century between the neighboring countries. This was worrisome as both India and Pakistan became nuclear powers.

Modern India

Hindus, Sikhs and Muslims live peacefully together in Delhi, for example, and this is primarily because most Hindus are peace-loving people who will go to any length not to fight. It is very difficult to fight someone who simply will not fight you for any reason. Also, Muslims follow the Koran very closely, and there is nothing in their book which says anything about the Hindu religion.