GK 2019 Q8
8. Andrew divided some apples into six equal piles. Boris divided the same number of apples into five equal piles. Boris noticed that each of his piles contained two more apples than each of Andrew’s piles. How many apples did Andrew have?
- A 30
- B 55
- C 60
- D 75
- E 90
Grey Kangaroo 2019, Question 8. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 60
Let the number of apples Andrew had be \(6n\). When Boris divided the same number of apples into five piles, each pile contained two more apples than each of Andrew’s piles. Therefore \(6n = 5(n + 2)\) and hence \(6n = 5n + 10\). This has solution \(n = 10\). Therefore the number of apples Andrew had was 6 × 10 = 60.
Solution © UK Mathematics Trust, from the GK 2019 solutions.