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

Working individually, A, B and C can  finish a piece of work in 16 days, 20 days  and 30 days respectively. In how many  days can A, B and C together complete  a work which is 3(1/2) times the previous  work?

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

Answered by 1549442205 last updated on 14/Jun/20

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

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

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