Question

A constructor want some men on voice to build a temple in a has to be completed in one month two men and 7 boys can do a price of work in 4 days, it is done by 4 men and 4 boys in 3 days. How would it take for one man or one boy to do it?​

Answer 1

1 man and 1 boy can complete the work in 36 days.

Step-by-step explanation:

Given, 2 men and 7 boys can do a piece of work in 4 day. It is done by by 4 men and 4 boys in 3 days.

Let, a men can do the work in x days and a boy can do the piece of work in y days.

Therefore work done by 1 boy in 1 day $=\frac{1}{y}$

                 work done by 7 boy in 1 day  $=\frac{7}{y}$

                 work done by 7 boy in 4 day$=\frac{7\times 4}{y}$ $=\frac{28}{y}$

                work done by 4 boy in 3 day$=\frac{4\times 3}{y}$$=\frac{12}{y}$

Similarly ,work done by 1 man in 1 day$=\frac {1}{x}$

               work done by 2 men in 1 day$=\frac{2}{x}$

               work done by 2 men in 4 day$=\frac{2\times4}{x}$$=\frac{8}{x}$

               work done by 4 men in 3 day$=\frac{4 \times 3}{x}$$=\frac{12}{x}$

According to the problem,

$4(\frac{28}{y}+\frac{8}{x})=1$                   and          $3(\frac{12}{y}+\frac{12}{x})=1$

 $\Rightarrow \frac{112}{y}+\frac{32}{x} =1$                            $\Rightarrow \frac{36}{y}+\frac{36}{x}=1$

Let  $\frac{1}{x} =u$  and  $\frac{1}{y} =v$

∴112v+32u=1   and  36 u+36v=1

Solving above two equation we get

   $u= \frac{19}{720}$     and  $v= \frac{1}{720}$

$\therefore \frac{1}{x} =\frac{19}{120}$     and   $\frac{1}{y} =\frac{1}{120}$

Work done by 1 man and 1 boy in 1 day $=\frac{19}{720} +\frac{1}{720}$

                                                                  $=\frac{20}{720}$

                                                                  = $\frac{1}{36}$

1 man and 1 boy can complete the work in 36 days.