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If 12 men can finish a task in 10 days, how many men are needed to finish it in 8 days?
15
18
20
12
15
Use the inverse proportion rule: Since time is reduced from 10 to 8 (a ratio of 5:4), the men required must increase by the reciprocal ratio (4:5). So, 12├Ч(5/4)=15.
12 men take 10 days to complete a task. We need to find the number of men required to complete the same task in 8 days.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the inverse proportion rule: Since time is reduced from 10 to 8 (a ratio of 5:4), the men required must increase by the reciprocal ratio (4:5). So, 12├Ч(5/4)=15.
Students often wrongly apply direct variation (M1тАЛ/D1тАЛ=M2тАЛ/D2тАЛ) instead of inverse variation, leading to the incorrect answer of 9.6.
Identify given variables
We are given the initial number of men M1тАЛ=12 and initial days D1тАЛ=10. The target days D2тАЛ=8.
M1тАЛ=12,D1тАЛ=10,D2тАЛ=8
Apply the Inverse Proportion Formula
The total work remains constant, so the product of men and days is equal in both scenarios: M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ.
12├Ч10=M2тАЛ├Ч8
Solve for M2
Isolate M2тАЛ by dividing the product by 8: M2тАЛ=8120тАЛ.
M2тАЛ=15
A is correct because calculating M2тАЛ=812├Ч10тАЛ yields 15 men required to complete the task.
This concept of inverse proportionality is also fundamental in Pipe and Cistern problems and Speed-Time-Distance problems involving constant distance.
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