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If 12 men or 18 women can reap a field in 14 days, how long will 8 men and 16 women take to reap the same field?
9 days
12 days
8 days
10 days
9 days
Convert all workers into a single unit (either all men or all women) using the equivalence ratio before computing total work.
12 men or 18 women can reap a field in 14 days. Find the time taken by 8 men and 16 women.
Time=Combined┬аEfficiencyTotal┬аWorkтАЛ
Convert all workers into a single unit (either all men or all women) using the equivalence ratio before computing total work.
Adding the number of men and women directly as raw integers without converting them to equivalent workers first.
Establish Efficiency Ratio
Since 12 men equal 18 women in work capacity, 1 man is equivalent to 23тАЛ women.
1┬аman=23тАЛ┬аwomen
Calculate Total Work
Total work in woman-days is given by multiplying the number of women by the days taken: 18├Ч14=252┬аwoman-days.
18├Ч14=252┬аwoman-days
Convert Workforce to Equivalent Women
Convert 8 men to equivalent women (8├Ч23тАЛ=12) and add the 16 women to get a total of 28┬аwomen.
8┬аmen+16┬аwomen=12+16=28┬аwomen
Compute Final Time
Divide the total work by the total equivalent workforce: 28252тАЛ=9┬аdays.
28252тАЛ=9┬аdays
A is correct because 8 men and 16 women equal 28 women, taking 9 days to complete the work.
The same efficiency equivalence principle applies to Pipes and Cisterns and Mixture problems.
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