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If 15 men can complete a work in 20 days, how many men are needed to complete it in 12 days?
20
25
30
18
25
Use the inverse proportionality relation between men and days: total man-days remain constant, so equating 15├Ч20=M2тАЛ├Ч12 directly gives M2тАЛ.
15 men can complete a work in 20 days. Time given to complete the work = 12 days.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the inverse proportionality relation between men and days: total man-days remain constant, so equating 15├Ч20=M2тАЛ├Ч12 directly gives M2тАЛ.
Students often mistakenly set up a direct proportion (i.e., fewer days means fewer men) instead of an inverse proportion.
Identify Total Work in Man-Days
The total amount of work required can be measured in man-days. Multiply the number of men by the number of days they take.
Total┬аWork=15├Ч20=300┬аman-days
Set Up Equation for 12 Days
Let the required number of men be x. The same total work of 300 man-days must be completed in 12 days.
x├Ч12=300
Calculate the Number of Men
Solve for x by dividing the total man-days by the target number of days.
x=12300тАЛ=25
B is correct because 25 men are required to complete the work in 12 days.
This inverse variation principle is also widely applicable in pipe and cistern problems where more pipes reduce the filling time.
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