Question

3 men and 6 boys can finish a piece of work in 3 days, while 2 men and 5 boys can finish it in 4 days. Then
time taken by one boy alone to finish the work is-​

Answer 1

Answer:

Hope it helps.

Thanks.

Answer 2

Given:

3 men and 6 boys can finish a piece of work in 3 days, and 2 men and 5 boys can finish it in 4 days.

To Find:

Time taken by one boy alone to finish work?

Step-by-step explanation:

• Let the number of days taken by a men and a boy be x and y days respectively.

• Therefore,work done by a men in 1 day=1/x

• work done by boy in 1 day = 1/y

A.T.Q

        $\bf 3(\frac{3}{x}+\frac{6}{y})=1\\and\\4(\frac{2}y{}+\frac{5}{y})=1$

 $\bf\textrm{put the value in above equation} \frac{1}{x}=a, \frac{1}{y}=b$

• then equations will become

       $3(3a+6b)=1 \\and\\4(2a+5b)=1$

• solving above euations by substitution method we get

      9a+18b=1 and 12a+5b=1

        $\bf a=\frac{1-18b}{9}\\\\\textrm{Put the value of a in another equation}\\\\8(\frac{1-8b}{9})+20b=1\\\\\frac{8-144b+180b}{9}=1\\\\\Rightarrow 8+36b=9\\\\\Rightarrow b=\frac{1}{36} \\\\Also\\a=\frac{1-18b}{9}\\\\\textrm { Put the value of b}\\\\a=\frac{1}{18}$

         $\bf a=\frac{1}{x}=\frac{1}{18}\\\\\Rightarrow x=18\\\\\bf b=\frac{1}{y}=\frac{1}{36}\\\\\Rightarrow y=36$

Hence time taken b y one boy to finish work is 36 days.