Question 478463
Let 1/b = part of the work done by one boy in one day, and 
let 1/m = part of the work done by one man in one day.

Then {{{(6/5)(4/m + 9/b) = 1}}}, and 
{{{(12/7)(3/m + 6/b) = 1}}}.

==> {{{4/m + 9/b = 5/6}}} and {{{3/m + 6/b = 7/12}}}
==> {{{1/m = 7/36 - 2/b}}} from the 2nd equation.

==> {{{4(7/36 - 2/b) + 9/b = 5/6}}}
==> {{{7/9 - 8/b + 9/b = 5/6}}} ==> {{{1/b = 5/6 - 7/9}}} ==>{{{1/b = 1/18}}}

==> 1/18 of the work is done per boy per day.

==> It will take 18 days for one boy to finish the work.