Question

​2 mens and 5 boys can do a piece of work in 4 days while 4 mens and 4 boys can do the same work in 3 days. How long would it take (i) 1 man alone to do it (ii) one boy alone to do it (iii) one man and one boy to do it

Answer 1

Dear Student,

$$\begin{gathered} Letthetimetakenbyamantodopieceofwork=xdays \\ andthetimetakenbyaboytodopieceofwork=ydays \\ Workdonebyamaninoneday=\frac{1}{x} \\ Workdonebyamaninoneday=\frac{1}{y} \\ Accordingtoquestion, \\ \frac{2}{x}+\frac{5}{y}=\frac{1}{4} \\ \&\frac{4}{x}+\frac{4}{y}=\frac{1}{3} \\ \Rightarrow \frac{4}{x}+\frac{10}{y}=\frac{2}{4} \\ \&\frac{4}{x}+\frac{4}{y}=\frac{1}{3} \\ Subtracting,weget \\ \frac{6}{y}=\frac{2}{4}-\frac{1}{3}=\frac{2}{12} \\ \Rightarrow \frac{6}{y}=\frac{1}{6} \\ \Rightarrow y=36 \\ Thus,\frac{4}{x}+\frac{4}{36}=\frac{1}{3} \\ \Rightarrow \frac{4}{x}+\frac{1}{9}=\frac{1}{3} \\ \Rightarrow \frac{4}{x}=\frac{1}{3}-\frac{1}{9}=\frac{2}{9} \\ \Rightarrow \frac{1}{x}=\frac{1}{18} \\ \Rightarrow x=18 \\ Thus,onemancandopieceofworkin18days \\ andoneboycandopieceofworkin36days. \end{gathered}$$

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