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If 15 men can finish a task in 20 days, how many men are needed to finish the same task in 12 days?
20
25
30
18
25
Use inverse proportionality: since the time is reduced from 20 to 12 (a factor of 5/3), the number of men must be increased by the reciprocal factor 3/5 of 20, which is multiplying 15 by 5/3.
15 men finish a task in 20 days. Required time to finish the same task is 12 days.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use inverse proportionality: since the time is reduced from 20 to 12 (a factor of 5/3), the number of men must be increased by the reciprocal factor 3/5 of 20, which is multiplying 15 by 5/3.
Students often incorrectly use direct proportion (M1тАЛ/D1тАЛ=M2тАЛ/D2тАЛ), which leads to the wrong answer of 9 men.
Identify given variables
Here, M1тАЛ=15, D1тАЛ=20, and D2тАЛ=12. We need to find M2тАЛ.
M1тАЛ=15,D1тАЛ=20,D2тАЛ=12
Set up the work equation
Since the total work remains constant, we equate the product of men and days for both scenarios.
15├Ч20=M2тАЛ├Ч12
Solve for the unknown
Isolate M2тАЛ by dividing the total man-days by the new time duration.
M2тАЛ=1215├Ч20тАЛ=12300тАЛ=25
B is correct because the calculation M2тАЛ=25 confirms that 25 men are required to complete the task in 12 days.
This concept of inverse variation is fundamental in pipe and cistern problems, where the rate of work (pipe capacity) is inversely proportional to the time taken to fill the tank.
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