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One man can do as much work in one day as a woman can do in 2 days A child does one-third the work in a day as a woman. If an estate-owner hires 39 pairs of hands, men, woman and children in the ratio 6 : 5 :2 and pays them in all Rs 1113 at the end of the day’s work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?

  1. Rs. 14 
  2. Rs. 5
  3. Rs. 20 
  4. Rs. 7
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First we find number of men , women and children . So :

           6x + 5x + 2x    =     39

==>     13x   =    39

==>     x      =     3

Hence number of men , women and children are 18 , 15 and 6 respectively.

According to the question , pay is done according to work done in one day . Now it is given , 

Work done by child  in  1 day    =    1/3 of woman 

Work done by woman  in  1 day   =   1/2 of man

Hence , 

              18 * 6x +  15 * 3x  + 6 * 1x     =    1113

==>        108 x +  45x +  6x                 =    1113

==>        159 x                                    =    1113

==>         x                                         =     1113 / 159

==>         x                                         =     7

Hence required amount to be paid to each child for each day    =   Rs

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