GK 2017 Q10
10. One sixth of an audience in a children's theatre are adults. Two fifths of the children are boys. What fraction of the audience are girls?
- A \(\dfrac{1}{2}\)
- B \(\dfrac{1}{3}\)
- C \(\dfrac{1}{4}\)
- D \(\dfrac{1}{5}\)
- E \(\dfrac{2}{5}\)
Grey Kangaroo 2017, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A \(\dfrac{1}{2}\)
One sixth of the audience are adults. Therefore five sixths of the audience are children. Two fifths of the children are boys and hence three fifths of the children are girls. Therefore three fifths of five sixths of the audience are girls. Now \(\tfrac{3}{5} \times \tfrac{5}{6} = \tfrac{1}{2}\). Hence the fraction of the audience who are girls is \(\tfrac{1}{2}\).
Solution © UK Mathematics Trust, from the GK 2017 solutions.