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$900$ men and $500$ woman complete a task in $2$ weeks. $1200$ men and $250$ woman took $3$ weeks to complete the same task. Then, how many men are required to complete the same task in $1$ week ?
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Best answer
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7 votes

Let  1 day task of 1 man = u

       1 day task of 1 woman = v

Then we have equations :

      900 u  +  500 v  =  1/14    [  As they complete in 14 days so 1 day work together = 1/14 ] ............(1)

      1200 u  + 250 v   =  1 / 21

==> 2400 u + 500 v   =  2 / 21   ..........(2)

Now (2) - (1) yields :

      1500 u   =  2/21 - 1/14

==> 1500 u  =  1 / 42

==>  u         =   1 / (42 * 1500)   is 1 man's 1 day work

So time taken by 1 man to complete work   =   1500 * 42 days  

                                                                =   1500 * 6 weeks

                                                                =    9000 weeks

Hence to get the work completed in 1 week :

No of men needed                                     =     9000 / 1

                                                                =    9000

Hence 9000 should be the correct answer

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4 votes
4 votes
Let man will finish same work in x weeks and womens will do the same in y weeks.
One week work :
900/x + 500/y = 1/2

2nd condition :
1200/x + 250/y = 1/3

1200/x + (500/y)/2 = 1/3
1200/x + ((1/2 - 900/x)/2 = 1/3
1200/x +1/4 -450/x) = 1/3
750/x = 1/12
x = 9000

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