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If 5 workers can complete a work in 12 days, how many days will 10 workers take to complete the same work?
6 days
8 days
10 days
4 days
6 days
Since the number of workers doubles (5 to 10), the time taken must be halved. Simply divide 12 by 2 to get 6.
Number of workers (M1) = 5, Number of days (D1) = 12, Number of workers (M2) = 10.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Since the number of workers doubles (5 to 10), the time taken must be halved. Simply divide 12 by 2 to get 6.
Students often wrongly assume a direct variation and calculate 5├Ч12/10 is wrong, but rather apply direct proportion like 5/12=10/x, forgetting that more workers take less time.
Identify Relationship
Since the work is constant, the number of workers is inversely proportional to the time taken.
MтИЭD1тАЛ
Apply Chain Rule Formula
Using the formula for work equivalence where M1тАЛD1тАЛ=M2тАЛD2тАЛ.
5├Ч12=10├ЧD2тАЛ
Solve for Days
Isolate D2тАЛ by dividing both sides by 10.
D2тАЛ=1060тАЛ=6
A is correct because the inverse relationship dictates that doubling the workers reduces the time required by half, resulting in 6 days.
This concept of inverse variation is fundamental to solving problems in pipe and cisterns, where more pipes result in less time to fill a tank.
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