10. Every pupil in a class either swims or dances. Three fifths of the class swim and three fifths dance. Five pupils both swim and dance. How many pupils are in the class?
A 15
B 20
C 25
D 30
E 35
Solution
C

Since three fifths of the class swim, three fifths of the class dance and no-one does neither, the fraction of the class who do both is $\frac{3}{5}+\frac{3}{5}-1=\frac{1}{5}$. Hence, since 5 pupils do both, the number of pupils in the class is $5 \times 5=25$.