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If 15 men can build a wall in 20 days, how many men are needed to build the same wall in 12 days?
20
25
30
18
25
Use the inverse proportionality relation: product of men and days remains constant (M1тАЛD1тАЛ=M2тАЛD2тАЛ), so M2тАЛ=1215├Ч20тАЛ=25.
Initial number of men M1тАЛ=15, Initial number of days D1тАЛ=20, Target number of days D2тАЛ=12
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the inverse proportionality relation: product of men and days remains constant (M1тАЛD1тАЛ=M2тАЛD2тАЛ), so M2тАЛ=1215├Ч20тАЛ=25.
Students often mistakenly set up a direct proportion ratio instead of inverse proportion, writing 15/20=M2тАЛ/12 instead of equating total man-days.
Understand the Concept of Man-Days
The total amount of work required to build the wall is constant and measured in man-days, which is the product of the number of men and the number of days they take.
Total┬аWork=M1тАЛ├ЧD1тАЛ
Set Up the Equation
Equate the total man-days for the initial scenario to the required man-days for the new scenario: 15├Ч20=M2тАЛ├Ч12.
15├Ч20=M2тАЛ├Ч12
Solve for the Unknown Men (M2тАЛ)
Rearrange the equation to solve for M2тАЛ: M2тАЛ=12300тАЛ=25.
M2тАЛ=12300тАЛ=25
B is correct because 25 men are needed to complete the same amount of work in 12 days.
This inverse proportionality concept is also heavily used in pipe and cistern problems as well as speed, time, and distance inverse variations.
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