A can do a work in 10 days and B can do the same work in 20 days. If both of them work together for 2 days, what fraction of the work is completed?
3/10
Take the total work as 1 unit.
A completes the work in 10 days, so A's one-day work is $\tfrac{1}{10}$. B completes it in 20 days, so B's one-day work is $\tfrac{1}{20}$.
Working together in one day they finish $\tfrac{1}{10}+\tfrac{1}{20}=\tfrac{2+1}{20}=\tfrac{3}{20}$ of the work.
In 2 days their combined output is $2\times\tfrac{3}{20}=\tfrac{6}{20}=\tfrac{3}{10}$ of the whole work.
Hence, 3/10.
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