India has two offical languages, Hindi and English, and 22 regional languages, among them Hindu and Sankrit. Speaches in parliament are delivered either in English or in a regional language, federal courts use English, law requires administration to increase the use of Hindi, although the authoritative version of all laws is English. To conclude: a gigantic mess.
Granted, the Indian situation is a complicated one. Hindi is the prevelant language, but not spoken by the whole country. English is the lingua franca of India, but English is the language of the former colonial oppressor and of the little Anglo-British community.
So, with a POD of after 1900, what about reviving Sanskrit as language of India beside the individual regional languages? Each federal states would have its own language, but the language for the federal level and the relations between the states would be Sanskrit, a neutral language; neutral because it is spoken by no individual group.
And as a joke, you can try to make the Indians adopt Greek as their official language after 1947, just to remember the great days of the Indo-Greeks and Kushans...