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If 15 men can complete a work in 20 days, how many days will 10 men take to complete the same work?
30 days
25 days
15 days
20 days
30 days
Since the number of men is reduced by a ratio of 15:10 (i.e., 3:2), the time taken must increase by the inverse ratio of 2:3. Multiply original days 20 by 3/2 to get 30.
15 men complete a work in 20 days. We need to find the days taken by 10 men.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Since the number of men is reduced by a ratio of 15:10 (i.e., 3:2), the time taken must increase by the inverse ratio of 2:3. Multiply original days 20 by 3/2 to get 30.
Students often use direct proportion (15/20=10/x) instead of inverse proportion, leading to an incorrect answer of 13.33 days.
Identify the relationship
Work and time are inversely proportional; as the number of men decreases, the time taken to complete the same work increases.
Work=Men├ЧDays
Set up the equation
Given M1тАЛ=15, D1тАЛ=20 and M2тАЛ=10. Let the required days be D2тАЛ. Substitute these into the formula M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ.
15├Ч20=10├ЧD2тАЛ
Solve for D2
Divide the total man-days (300) by the number of men (10).
D2тАЛ=10300тАЛ=30
A is correct because 10 men will take 30 days to complete the work as calculated using the inverse proportionality principle.
This concept of inverse proportionality is identical to problems involving tap filling/emptying rates and distance-speed-time calculations where distance is constant.
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