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If 12 men can build a wall in 20 days, how many men are needed to build the same wall in 15 days?
16
18
15
20
16
Use the inverse proportionality ratio of days (20:15=4:3), so the number of men required scales in the inverse ratio (3:4), giving 34тАЛ├Ч12=16 men.
Number of men initially (M1тАЛ) = 12, Days taken initially (D1тАЛ) = 20 days, Target days (D2тАЛ) = 15 days
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the inverse proportionality ratio of days (20:15=4:3), so the number of men required scales in the inverse ratio (3:4), giving 34тАЛ├Ч12=16 men.
Students often set up a direct proportion (e.g., multiplying 12 by 15/20) assuming fewer days require fewer men, forgetting that time and workers are inversely proportional.
Understand the Inverse Relationship
Since fewer days require more men to complete the same amount of work, the number of men and the number of days are inversely proportional.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Substitute the Given Values
Substitute the given values M1тАЛ=12, D1тАЛ=20, and D2тАЛ=15 into the inverse proportion equation.
12├Ч20=M2тАЛ├Ч15
Calculate the Required Number of Men
Solve for M2тАЛ by isolating it on one side of the equation: M2тАЛ=1512├Ч20тАЛ=15240тАЛ=16.
M2тАЛ=15240тАЛ=16
A is correct because 16 men are required to build the wall in 15 days.
This inverse proportionality principle is widely applicable in pipes and cisterns as well as general arithmetic problems involving speed and time.
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