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If 15 men can complete a work in 20 days, how many men are needed to complete the same work in 12 days?
25
20
18
30
25
Use the inverse ratio of days: Days decrease in the ratio 20:12 (or 5:3), so men must increase in the ratio 3:5. 15├Ч(5/3)=25.
15 men complete a work in 20 days. We need to find the number of men to complete the same work in 12 days.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the inverse ratio of days: Days decrease in the ratio 20:12 (or 5:3), so men must increase in the ratio 3:5. 15├Ч(5/3)=25.
Students often use direct proportion (15/20 = x/12) instead of inverse proportion, forgetting that fewer days require more men.
Identify the relationship
Since the total work remains constant, the number of men is inversely proportional to the number of days taken.
Work=Men├ЧDays
Set up the equation
Using the formula M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ, where M1тАЛ=15, D1тАЛ=20, and D2тАЛ=12.
15├Ч20=M2тАЛ├Ч12
Solve for M2тАЛ
Divide both sides by 12 to isolate M2тАЛ.
M2тАЛ=1215├Ч20тАЛ=12300тАЛ=25
A is correct because calculation results in 25 men being required to complete the work in 12 days.
This concept of inverse variation is fundamental in Pipe and Cistern problems, where increasing the number of pipes decreases the time to fill a tank.
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