Since all the students who liked pizza also liked Chinese, and no student liked all three, we can just think about the remaining $25$ students.
Of these, $14$ liked Chinese and $16$ liked Indian. Since each student liked at least one of these, and there are a total of $30$ 'likes', $5$ students must like both Indian and Chinese.
This leaves $11$ students who liked Indian only.
This problem is taken from the UKMT Mathematical Challenges.