Question

# A can do a piece of work in 24 days while B can do it in 30 days. In how many days can they complete it, if they work together ?

Solution

## Let total works $$=x$$$$A$$ takes $$24\ days$$ to complete $$x$$$$\Rightarrow$$ In one day a complete work $$=\dfrac{x}{24}$$$$B$$ completes $$x$$ works in $$30\ days$$$$\Rightarrow$$ In $$1$$ day $$B$$ completes work $$=\dfrac{x}{30}$$If $$A$$ and $$B$$ work together,work done in one day $$=\dfrac{x}{24}+\dfrac{x}{30}$$$$=\dfrac{5x+4x}{120}=\dfrac{9x}{120}=\dfrac{3x}{40}$$Let they take $$n$$ days to complete entire work.$$\Rightarrow$$ Total work $$=n\times \dfrac{3x}{40}=x$$$$\Rightarrow n=\dfrac{40}{3}\ days$$Mathematics

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