A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

12 days
15 days
16 days
18 days

Correct answer: 15 days

Solution

A does $\frac{1}{20}$ per day, B does $\frac{1}{30}$, and C does $\frac{1}{60}$. In 3 days, work done = $2\cdot\frac{1}{20}+\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{60}\right)=\frac{1}{10}+\frac{1}{10}=\frac{1}{5}$, so 5 such cycles are needed. Total time = $5\times 3=15$ days.

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