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Question Number 98464 by Vishal Sharma last updated on 14/Jun/20

$$\mathrm{Working}\mathrm{individually},\mathrm{A},\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{can}$$$$\mathrm{finish}\mathrm{a}\mathrm{piece}\mathrm{of}\mathrm{work}\mathrm{in}16\mathrm{days},20\mathrm{days}$$$$\mathrm{and}30\mathrm{days}\mathrm{respectively}.\mathrm{In}\mathrm{how}\mathrm{many}$$$$\mathrm{days}\mathrm{can}\mathrm{A},\mathrm{B}\mathrm{and}\mathrm{C}\mathrm{together}\mathrm{complete}$$$$\mathrm{a}\mathrm{work}\mathrm{which}\mathrm{is}3\frac{1}{2}\mathrm{times}\mathrm{the}\mathrm{previous}$$$$\mathrm{work}?$$

Answered by 1549442205 last updated on 14/Jun/20

$$$$$$$$$$\mathrm{in}\mathrm{a}\mathrm{day}\overline{\mathrm{A}},\mathrm{B},\mathrm{C}\mathrm{every}\mathrm{person}\mathrm{do}\frac{1}{16},\frac{1}{20},\frac{1}{30}\left(\mathrm{work}\right)$$$$\mathrm{respectively}.\mathrm{It}\mathrm{follows}\mathrm{that}\mathrm{if}\mathrm{working}\mathrm{together}$$$$\mathrm{they}\mathrm{will}\mathrm{work}\frac{1}{16}+\frac{1}{20}+\frac{1}{30}=\frac{15+12+8}{240}=\frac{7}{48}\left(\mathrm{work}\right)$$$$\mathrm{Hence},\mathrm{to}\mathrm{complete}\mathrm{a}\mathrm{work}\mathrm{equal}\mathrm{to}3\frac{1}{2}\mathrm{times}$$$$\mathrm{previous}\mathrm{work}\mathrm{they}\mathrm{need}3\frac{1}{2}:\frac{7}{48}=24\left(\mathrm{day}\right)$$$$24\mathrm{days}\mathrm{is}\mathrm{the}\mathrm{answer}\mathrm{of}\mathrm{our}\mathrm{problem}.$$$$$$

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