Chemerical71 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.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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