Takeaway time

Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?

Problem



$35$ teenagers were asked what takeaways they liked to eat.

 

$24$ answered Chinese
$16$ answered Indian
$10$ answered pizza


None of the teenagers liked all three.

All who liked pizza also liked Chinese.

$9$ of the Chinese fans didn't like either Indian or pizza.

 

If all the teenagers liked at least one, how many liked only Indian?