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If 5 workers can build a wall in 10 days, how many workers are needed to build it in 5 days?
8
10
12
15
10
Since the number of days is halved (from 10 to 5), the number of workers must be doubled to keep the total work constant.
Number of workers (W1) = 5, Time taken (D1) = 10 days. Target time (D2) = 5 days.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Since the number of days is halved (from 10 to 5), the number of workers must be doubled to keep the total work constant.
Students often incorrectly apply direct proportion, calculating (5├Ч5)/10=2.5 instead of realizing that fewer days require more workers.
Identify Relationship
Since the amount of work remains constant, the number of workers is inversely proportional to the time taken.
Work=Workers├ЧDays
Set up the Equation
Equating the total man-days required for both scenarios:
5├Ч10=M2тАЛ├Ч5
Solve for Required Workers
Divide both sides by 5 to isolate the number of workers required:
M2тАЛ=550тАЛ=10
B is correct because calculating the inverse proportion yields a requirement of 10 workers to complete the work in half the time.
This inverse variation principle is also foundational for solving problems related to pipes and cisterns (rate of flow vs time) in competitive exams.
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