Question

who had invented badminton and why​

Answer 1

Invented in India in a version called poona. British army officers learned the game about 1870. In 1873 the duke of Beaufort introduced the sport at his country estate, Badminton, from which the game derives its name.

Answer 2

Badminton is first known to be played in Pune India by British officers during British rule in India.

And I think they started playing it for fun.