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, women and children in the ratio 6 : 5 : 2 and pays them in all rs. 1113 at the end of the days work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?
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Answer:
The daily wage of a child = rs. 7
Step-by-step explanation:
Let amount of work done in a day by
Man = x
Woman = 1/2 x
Child = 1/3(1/2x) = 1/6x
Each person has a pair of hands. So, 39 pairs of hands = 39 people
The ratio Men: Women : Children = 6 : 5 ; 2
Total ratio = 6 + 5 + 2 = 13
Number of men = 6/13 x 39 = 18
Number of women = 5/13 x 39 = 15
Number of children = 2/13 x 39 = 6
Work done by men = 18x
Work done by women = 15(1/2x) = 15/2 x
Work done by children = 6(1/6x) = x
Total work done = 18x + 15/2x + x = 53/2 x
Children's wage = x/(53/2 x) x 1113 = rs. 42
The daily wage of a child = 42/6 = rs. 7
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