Question 985130

From the given data, the rate of work for  1  worker per  1  day is   {{{12/(16*6)}}} = {{{12/96}}} = {{{1/8}}} {{{cupboards/(worker*day)}}}.

In other words,  1  worker paints  {{{1/8}}}  of a cupboard per day.


(We assume that all workers have the same rate of work and that all cupboards are identical). 


If 12 workers paint &nbsp;45&nbsp; cupboards in &nbsp;<B>x</B>&nbsp; days, then their rate of work is &nbsp;{{{45/(12*x)}}} {{{cupboards/(worker*day)}}}. 


It the same rate of work as calculated above, i.e. {{{1/8}}} {{{cupboards/(worker*day)}}}.

Thus you have an equation 


{{{45/(12*x)}}} = {{{1/8}}}.


Hence, &nbsp;x = {{{(45*8)/12}}} = {{{30}}} days. 


<B>Answer</B>. &nbsp;{{{30}}} days.