PK 2017 Q11
11. A belt drive system consists of the wheels \(K\), \(L\) and \(M\), which rotate without any slippage. The wheel \(L\) makes 4 full turns when \(K\) makes 5 full turns; also \(L\) makes 6 full turns when \(M\) makes 7 full turns.
The perimeter of wheel \(M\) is 30 cm. What is the perimeter of wheel \(K\)?
- A 27 cm
- B 28 cm
- C 29 cm
- D 30 cm
- E 31 cm
Pink Kangaroo 2017, Question 11. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 28 cm
To compare wheels \(K\) and \(M\), we need to find the lowest common multiple of 4 and 6, which is 12. When wheel \(L\) makes 12 turns, wheel \(K\) makes 15 turns and wheel \(M\) makes 14 turns. When wheel \(L\) makes 24 turns, wheel \(K\) makes 30 turns and wheel \(M\) makes 28 turns, so the ratio of the circumferences of wheel \(K\) to wheel \(M\) is 28:30.
Solution © UK Mathematics Trust, from the PK 2017 solutions.