Why the british came and ruled iNDIA?

The simple answer is: Profit. Certainly at first that was the primary reason. The East Indian Company had a charter from the crown giving them a monopoly over trade with India. Investors in England could make a large profit from every ship that came back loaded with exotic cargo, especially silk cloth and spices. People could by shares in an expedition, much like the stock market works today, allowing people of more modest means to participate and spreading the risks.
The East Indian Company got involved with Indian politics almost by accident; they would lend aid to whatever mullah or faction furthered their goals, and support the opposition against whoever defied them. Their resources and access to British rifles, cannon, and warships made them powerful players.
After a century, they were the power behind many thrones, and the interests of the Company became identical to the interests of Parliament (especially since many of the main investors and Board members of the company were powerful men in the British government.). Eventually it got to the point where the Crown saw fit to take direct control and annex India into the Empire.