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If 12 men can complete a piece of work in 18 days, in how many days can 8 men complete the same work?
27 days
24 days
30 days
25 days
27 days
Use the ratio method: The ratio of men changes from 12 to 8 (i.e., 3:2). Since men and days are inversely proportional, the ratio of days changes from 2:3. Since 2 units = 18 days, 1 unit = 9 days, so 3 units = 27 days.
12 men take 18 days to complete a work. We need to find the number of days for 8 men to complete the same work.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the ratio method: The ratio of men changes from 12 to 8 (i.e., 3:2). Since men and days are inversely proportional, the ratio of days changes from 2:3. Since 2 units = 18 days, 1 unit = 9 days, so 3 units = 27 days.
Students often mistakenly set up a direct proportion (12/18 = 8/x), resulting in the wrong answer; remember that work capacity is inversely proportional to the number of people.
Identify the relationship
Since the total work remains constant, the product of the number of men and days is equal in both scenarios.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Substitute the known values
Substitute M1тАЛ=12, D1тАЛ=18, and M2тАЛ=8 into the formula to find D2тАЛ.
12├Ч18=8├ЧD2тАЛ
Calculate the unknown variable
Solve for D2тАЛ by dividing the product by 8: D2тАЛ=812├Ч18тАЛ.
D2тАЛ=8216тАЛ=27
A is correct because 12 men working for 18 days results in 216 man-days, which requires 27 days for 8 men to complete the same work.
This concept of inverse proportionality is also used in 'Speed, Distance, and Time' problems where speed is inversely proportional to time for a fixed distance.
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