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If 12 men can finish a project in 10 days, how many men are needed to finish the same project in 8 days?
15
18
12
20
15
Use the inverse proportionality rule: Since days decreased from 10 to 8 (a ratio of 5:4), the men must increase by the reciprocal ratio 4:5. Multiply 12 by (10/8) to get 15.
Initial men (M1) = 12, Initial days (D1) = 10, Target days (D2) = 8.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the inverse proportionality rule: Since days decreased from 10 to 8 (a ratio of 5:4), the men must increase by the reciprocal ratio 4:5. Multiply 12 by (10/8) to get 15.
Students often set up a direct proportion (12/10 = x/8) instead of an inverse proportion, leading to an incorrect result of 9.6.
Identify Relationship
Since the work remains constant, the number of men is inversely proportional to the number of days.
Work=Men├ЧDays
Set up the equation
Using the chain rule formula M1тАЛD1тАЛ=M2тАЛD2тАЛ, substitute the given values M1тАЛ=12, D1тАЛ=10, and D2тАЛ=8.
12├Ч10=M2тАЛ├Ч8
Calculate the result
Solve for M2тАЛ by dividing the total man-days by the new number of days: M2тАЛ=120/8.
M2тАЛ=15
A is correct because calculating 120 man-days divided by 8 days yields 15 men required.
This concept of inverse variation is identical to speed-time calculations where distance is constant, helping you solve both time-work and speed-distance problems quickly.
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