A can do a piece of work in 10 days while B alone can do it in 15 days. In how many days can both finish the same work?

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A can do a piece of work in 10 days while B alone can do it in 15 days. In how many days can both finish the same work?

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Number of days A required do a piece of work : 10

Number of days B required do a piece of work : 15

Work done by A in one day: $\frac{1}{10}$

Work done by B in one day: $\frac{1}{15}$

Work done by A and B together in one day: $\frac{1}{10}+\frac{1}{15}=\frac{5}{30}=\frac{1}{6}$

∴ They can do the work together in 6 days.