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If 15 men can complete a work in 20 days, how many days will 20 men take to complete the same work?
10 days
15 days
18 days
25 days
15 days
Since work is constant, use the inverse ratio of men: 15:20=3:4. The ratio of days will be 4:3. Since 4 units corresponds to 20 days (1 unit = 5 days), then 3 units =15 days.
15 men complete work in 20 days. Find the time taken by 20 men for the same work.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Since work is constant, use the inverse ratio of men: 15:20=3:4. The ratio of days will be 4:3. Since 4 units corresponds to 20 days (1 unit = 5 days), then 3 units =15 days.
Confusing direct and inverse variation; students often try to divide 20 by 15 or assume more men take more days, whereas man-power and time are inversely proportional.
Define variables
Let M1тАЛ=15, D1тАЛ=20, M2тАЛ=20, and D2тАЛ be the number of days required by 20 men.
M1тАЛ=15,D1тАЛ=20,M2тАЛ=20,D2тАЛ=x
Apply Inverse Proportion formula
Because work done is constant, we use the product relationship M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ.
15├Ч20=20├Чx
Calculate the result
Solve for x by dividing both sides by 20.
x=2015├Ч20тАЛ=15
B is correct because the calculation 15├Ч20=20├Чx yields x=15 days.
This concept of inverse proportionality also applies to speed-time calculations, where Distance=Speed├ЧTime.
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