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Question Number 127607 by bramlexs22 last updated on 31/Dec/20

Answered by liberty last updated on 31/Dec/20

$$\mathrm{A}\Rightarrow 24\mathrm{days}$$$$\mathrm{B}\Rightarrow 15\mathrm{days}$$$$\mathrm{C}\Rightarrow 12\mathrm{days}$$$$\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{started}\mathrm{worked}3\mathrm{days}\Rightarrow 3\times (\frac{1}{15}+\frac{1}{12})\mathrm{work}$$$$\Rightarrow \frac{1}{5}+\frac{1}{4}=\frac{9}{20}\mathrm{works}$$$$\mathrm{remaining}\mathrm{works}=1-\frac{9}{20}=\frac{11}{20}$$$$\mathrm{A}\mathrm{complete}\mathrm{the}\mathrm{remaining}\mathrm{works}\Rightarrow \mathrm{n}\times \frac{1}{24}=\frac{11}{20}$$$$\Rightarrow \mathrm{n}=\frac{\cancel{24}{}^6\times 11}{\cancel{20}{}^5}=\frac{66}{5}\mathrm{days}=13\frac{1}{5}\mathrm{days}$$

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