There wasn't a border in India. The borders drawn were NOT made by the British, but by Mohammed Ali Jinnah & Pandit Jawaharlal Nehru. Where there was a Muslim majority, that was Pakistan (hence W. Pakistan & E. Pakistan, which later became Bangladesh). Where there was a Hindu majority became India. Where the situation was mixed, the state in question was allowed to choose. In Princely States, that meant the ruler choosing (hence Jammu & Kashmir going to India; the province is about 60% Muslim, but the Princely dynasty was Hindu). The only thing for the British to do was to approve the final decisions, which they did. The fact that there was no natural border is indicated by the fact that Punjab, home of the Sikhs, was divided in half. They weren't considered by either Muslims or Hindus. If India's borders had been drawn by the British, Punjab would probably be independent.