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# Twenty-four men can complete a work in sixteen days.Thirty-two women c

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Intern
Joined: 31 Dec 2017
Posts: 19
Concentration: Finance
Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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14 Jan 2018, 19:00
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

Total work $$= 24m*16d = 384md$$, or $$32w * 24d = 768wd$$.

$$24m * 16d = 32w * 24d$$
$$1md = 2wd$$: men are twice as efficient as women.

Work done by $$16m$$ and $$16w$$ in $$12$$ days $$= 12(32wd + 16wd) = 576wd$$.

Remaining work $$= 768-576 = 192 wd$$, can be completed in $$2$$ days by $$\frac{192}{2} = 96w$$.

$$96w - 48w = 48w = 24m$$. Ans - B.
Intern
Joined: 27 Nov 2017
Posts: 1
Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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26 Mar 2018, 00:04
24m*16=32w*24
m=2w
16m+16w=48w
48w 12 dasy works =12*48/32*24
=3/4
the rest =1/4
1/4 works in 2 days need
=48*12*4/3*4*2
=96 w
2w = 1 m
96w=48 m
here original m 24
so extra m 48-24
24

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Joined: 12 Oct 2010
Posts: 186
Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c  [#permalink]

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09 Sep 2018, 09:18
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.
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Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

Re: Twenty-four men can complete a work in sixteen days.Thirty-two women c &nbs [#permalink] 09 Sep 2018, 09:18

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