GK 2020 Q10
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
Grey Kangaroo 2020, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 25
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 \(\tfrac{3}{5} + \tfrac{3}{5} - 1 = \tfrac{1}{5}\). Hence, since 5 pupils do both, the number of pupils in the class is 5 × 5 = 25.
Solution © UK Mathematics Trust, from the GK 2020 solutions.