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UKMT Pink Kangaroo, 2017

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

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) $27\text{ cm}$ (B) $28\text{ cm}$ (C) $29\text{ cm}$ (D) $30\text{ cm}$ (E) $31\text{ cm}$

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