Question

# Suppose $$A$$ is twice as good a workman as $$B$$ and together they can finish a job in $$24$$ days. How many days $$A$$ alone takes to finish the job?

Solution

## $$A$$ is twice a good workman as $$B$$$$\therefore B=2A$$It is given that $$A$$ and $$B$$ together can finish the job in $$24$$ days.$$\therefore \dfrac{1}{A}+\dfrac{1}{B}=\dfrac{1}{24}$$Substituting $$B=2A$$ we get$$\therefore \dfrac{1}{A}+\dfrac{1}{2A}=\dfrac{1}{24}$$$$\Rightarrow \dfrac{2+1}{2A}=\dfrac{1}{24}$$ Taking LCM$$\Rightarrow \dfrac{3}{2A}=\dfrac{1}{24}$$ Cross multiplying we get,$$\Rightarrow 3*24=2A$$$$\Rightarrow A=\dfrac{72}{2}$$ $$\Rightarrow A=36$$Therefore $$A$$ alone can finish the work in $$36$$ days.Mathematics

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