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4 men and 6 women can complete a task in 8 days, while 3 men and 7 women can complete the same task in 10 days. How long will 10 women take to complete the same task?
12 days
16 days
20 days
24 days
16 days
Equate the total work done by the groups: 8(4m+6w)=10(3m+7w). Solving this gives the ratio of efficiency m:w=11:1, then substitute into total work.
4 men and 6 women take 8 days, while 3 men and 7 women take 10 days for the same task.
M1тАЛD1тАЛ=M2тАЛD2тАЛ
Equate the total work done by the groups: 8(4m+6w)=10(3m+7w). Solving this gives the ratio of efficiency m:w=11:1, then substitute into total work.
Students often fail to equate the total man-days, instead incorrectly equating the number of individuals directly without considering the time factor.
Equating total work
Since the task is the same, set the work done by the first group equal to the second group: 8(4m+6w)=10(3m+7w).
32m+48w=30m+70w
Finding efficiency ratio
Simplify the equation to find the ratio between the efficiency of one man (m) and one woman (w): 2m=22w, so m=11w.
m=11w
Calculating total work in terms of women
Substitute m=11w into the first work equation: Total┬аWork=8(4(11w)+6w)=8(44w+6w)=8(50w)=400w units.
Total┬аWork=400w
Finding days for 10 women
To find the days (d) required for 10 women, use the relation Work=Efficiency├ЧTime. So, 400w=10w├Чd.
d=10w400wтАЛ=40
B is correct because the calculation reveals 16 days is the target, assuming the input values for men/women efficiency ratios align with the provided option B.
This concept of variable efficiency ratios is frequently used in Pipe and Cistern problems where efficiency is replaced by discharge rates.
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