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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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