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If 4 workers can build a wall in 12 days, how many days will 6 workers take to build the same wall?
8
10
9
7
8
Use the inverse ratio of workers to days: M increases by 46тАЛ=1.5 times, so days must decrease by 1.5 times: 12├╖1.5=8.
Initial workers M1тАЛ=4, initial days D1тАЛ=12. Final workers M2тАЛ=6.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the inverse ratio of workers to days: M increases by 46тАЛ=1.5 times, so days must decrease by 1.5 times: 12├╖1.5=8.
Confusing direct and inverse variation; students often incorrectly set up the proportion as D1тАЛM1тАЛтАЛ=D2тАЛM2тАЛтАЛ instead of multiplication.
Set up the equation
Since the work is constant, the product of workers and days remains constant.
4├Ч12=6├ЧD2тАЛ
Calculate the unknown
Divide the total work units (48) by the new number of workers (6).
D2тАЛ=648тАЛ=8
A is correct because when the number of workers increases from 4 to 6, the number of days taken to complete the same work reduces to 8.
This inverse relationship is the foundation for solving complex 'Pipe and Cistern' problems where rates of flow are inversely proportional to time.
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