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UKMT Senior Mathematical Challenge, 2017

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

Amy, Beth and Claire each has some sweets. Amy gives one third of her sweets to Beth. Beth gives one third of all the sweets she now has to Claire. Then Claire gives one third of all the sweets she now has to Amy. All the girls end up having the same number of sweets. Claire begins with 40 sweets. How many sweets does Beth have originally?

(A) $20$ (B) $30$ (C) $40$ (D) $50$ (E) $60$

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