Jawaharlal Nehru, the son of a powerful Congress leader, became the first Prime Minister of the newly independent country of India, and Liaquat Ali Khan was the first Prime Minister of Pakistan. A large mountainous border area between India, China, Afghanistan, and Pakistan - Kashmir, and all of north-western Pakistan - remained disputed, and for the most part answered only to local rulers.
Ayub Khan of Pakistan
Both countries looked for powerful allies, and India (like its neighbors Afghanistan and Iran) began to get help from Russia, while Pakistan got help from the United States. As Russia preferred, India followed more socialist policies, with the government owning or controlling a lot of businesses. Pakistan, to please the United States, took a more capitalist path, with most of its rulers coming from the military. By 1954, Pakistan was under martial law; the general Ayub Khan took power in 1958.
When Nehru died in 1964 with no sons, his daughter, Indira Gandhi, almost immediately succeeded him; she held power in India until 1984. Her power reflects the influence of Central Asian, Communist feminism, and she continued her father's policy of being allied with Russia, and enriching their own family and friends.
In 1971, with Indira Gandhi's support, East Pakistan fought a war to become an independent country, Bangladesh. Bangladesh wanted to be more socialist than Pakistan - more like India. At first Bangladesh was very poor, and there were famines, but .
At the same time, the socialist People's Party also took power in Pakistan under Zulfikar Ali Bhutto on the promise of redistribution of land. Pakistan began to move away from the United States and closer to Russia and China. When army generals killed Bhutto in 1979, his daughter Benazir Bhutto took over in 1988. Struggles continued between the army generals (mostly favoring the United States) and the socialist party.
In 1984, Indira Gandhi's own Sikh bodyguards killed her. Her son Rajiv Gandhi took power. As the Soviet Union collapsed, Rajiv turned India's alliance from Russia to the United States, and began changing to more capitalist policies. These policies led to rapid economic growth, but also growing inequality, with the rich getting richer and the poor getting poorer.
But a Tamil independence fighter killed Rajiv in 1991. For the next twenty years, more conservative Hindu politicians - also capitalists, but capitalists who favor Hindus over Sikhs, Muslims, Christians, and Parsees - struggled to get control of India, but in 2004 Rajiv's widow, Sonia Gandhi, won an election. She didn't rule herself, but left power to her ally Manmohan Singh, a Sikh. However, in 2014, the Hindu conservatives won a sweeping victory in the elections, and for now, the Gandhi family is out of power again. India is getting richer, but more unequal and more sexist and racist.
Things are even worse in Pakistan: after Benazier Bhutto was killed in 2007, General Musharraf became unpopular and resigned. The government has become weaker and weaker, and more and more of Pakistan has fallen under the control of the Taliban or local clan leaders.
Bangladesh has been doing relatively well. Since 1991, Bangladesh has had an elected democratic government, currently under Sheikh Hasina, and has been building schools and health clinics and roads. Sadly, all of this is threatened by global warming; Bangladesh will soon suffer from terrible floods caused by rising sea levels.