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If 8 workers finish the work for 12 days, for how many days the same work will be finished from 4 workers?

I think that the correct answer is 24 days but in a book where I copied this question the correct question that is marked is 6.

Thank you

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BTW, $\,24\,$ days is the correct answer... – DonAntonio Apr 20 '13 at 18:42
@Enve: Even before starting to solve anything, that answer doesn't make any sence: more workers should do the job in less time (unless the additional 4 workers just prevent the others from working...) – Dennis Gulko Apr 20 '13 at 18:44
Depends on the kind of work. If the work is to wash every worker, $4$ workers will still take $12$ days. If the work is to shake every other worker's hand, $4$ workers will only take $\frac{3}{7}\cdot 12$ days. – Abel Apr 20 '13 at 18:45
this is a university sample... look at the 9 question – Enve Apr 20 '13 at 18:52
@DennisGulko did you mean sense – Enve Apr 20 '13 at 19:12
up vote 2 down vote accepted


(1) In one day eight workers do $\,1/12$-th of the total work, so each workers does

$$\frac{\frac{1}{12}}{8}=\frac{1}{96}\,\text{- th of the work each day}$$

(2) Four workers thus do

$$4\frac{1}{96}=\frac{1}{24} -\text{- th of the work each day}$$

so how many days do they need to finish the work?

The above is the general setting for these problems. In the present case there is, of course, a much simpler approach: $\,4\,$ workers will finish the work in twice the time as $\,8\,$ workers...

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this is a university sample... look at the 9 question – Enve Apr 20 '13 at 18:55
Well, I guess anyone can call anything "university" or whatever exercises. The ones in that link are junior high school and high school mathematics, perhaps (and hopefully!) for people who is not going to study sciences in that university. – DonAntonio Apr 20 '13 at 19:02
you are right, this is a test to get merit scholarship and issued by the university, that was the reason I called it "university". I didn't said that the mathematical tasks are for university students – Enve Apr 20 '13 at 19:07

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