BTGmoderatorDC wrote:Twenty-four men can complete a work in sixteen days.Thirty-two women can complete the same work in twenty-four days.Sixteen men and sixteen women started working for twelve days.How many more men are to be added to complete the work remaining work in 2 days?
A .16
B. 24
C. 36
D. 48
E. 54
Nice problem!
Let´s suppose each man does 1 task/day , and each woman does k tasks/day (where k>0, not necessarily an integer).
By the question stem, we know that:
> 24 men do 1 work in 16 days, hence 1 work = 24*16 tasks (1)
> 32 women do 1 work in 24 days, hence 1 work = 32*24*k tasks implies, by (1) above, that k = 1/2
> 16 men and 16 women will do in 12 days exactly 16*12*1 + 16*12*1/2 = 24*12 tasks, therefore by (1) we have still 24*(16-12) = 24*4 tasks to be done.
> If x is the number of men to be added (our
FOCUS), we have a group of (16+x) men and 16 women performing (16+x)*1 + 16*1/2 = (24+x) tasks/day , and the final touch is done
with UNITS CONTROL, one of our method´s most powerful tools:
\[24 \cdot 4\,\,\,{\text{tasks}}\,\,\, = \,\,2\,\,days\,\,\left( {\frac{{24 + x\,\,\,{\text{tasks}}}}{{1\,\,\,{\text{day}}}}\,\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,24 + x = 24 \cdot 2\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = x = 24\]
Obs.: arrows indicate
licit converters.
(If you realize this solution is absolutely clear and safe, you are the perfect candidate for our method... try our free and super-complete test drive!)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
