UPSC NDA I 2015 Mathematics Solved Paper

Let ‘A’ stand for the set of students who like dancing.
Let ‘B’ stand for the set of students who like music.
Applying set theory we get
n(A∪B)=n(A)+n(B)−n(A∩B)
(60−5)=45+50−n(A∩B)
n(A∩B)=95−55
n(A∩B)=40
Hence the set of students who like both are 40.