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If 12 men or 18 women can reap a field in 14 days, how long will 8 men and 9 women take to reap the same field?
12┬аdays
10┬аdays
9┬аdays
14┬аdays
12┬аdays
Convert men to equivalent women using the efficiency ratio 2M=3W, then apply the inverse proportion formula W1тАЛD1тАЛ=W2тАЛD2тАЛ.
12 men or 18 women can reap a field in 14 days. Find the time taken by 8 men and 9 women.
Days=W2тАЛW1тАЛ├ЧD1тАЛтАЛ
Convert men to equivalent women using the efficiency ratio 2M=3W, then apply the inverse proportion formula W1тАЛD1тАЛ=W2тАЛD2тАЛ.
Directly adding the number of men and women (8 + 9 = 17) without converting them to a common efficiency unit.
Establish Work Equivalence
Since 12 men do the same work as 18 women in the same time, we equate their efficiencies: 12M=18W, which simplifies to 2M=3W.
12M=18WтЯ╣2M=3W
Convert Combined Workers to a Single Unit
Convert the 8 men into equivalent women: 8M=8├Ч23тАЛ=12W. Adding the 9 women gives a total of 12W+9W=21W.
8M+9W=12W+9W=21W
Calculate Time Taken
Using inverse proportionality, 18 women take 14 days, so 21 women take D2тАЛ=2118├Ч14тАЛ=12 days.
D2тАЛ=2118├Ч14тАЛ=318├Ч2тАЛ=12┬аdays
A is correct because 8 men and 9 women are equivalent to 21 women, who will take 12 days to reap the field.
Mastering efficiency ratios helps solve complex pipes, cisterns, and mixed-proportion problems effortlessly across competitive exams.
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