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If 12 workers can complete a project in 20 days, how many workers are needed to complete the same project in 15 days?
15
16
18
20
16
Use the ratio of days: Since days decrease from 20 to 15 (a ratio of 4:3), the number of workers must increase in the inverse ratio (3:4). Applying this, 12├Ч(4/3)=16.
12 workers can complete a project in 20 days. We need to find the workers required for 15 days.
M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ
Use the ratio of days: Since days decrease from 20 to 15 (a ratio of 4:3), the number of workers must increase in the inverse ratio (3:4). Applying this, 12├Ч(4/3)=16.
Students often wrongly assume a direct proportion (12/20=x/15), whereas time and work are inversely proportional; as days decrease, worker count must increase.
Identify parameters
Let M1тАЛ=12 (initial workers), D1тАЛ=20 (initial days), D2тАЛ=15 (new days), and M2тАЛ be the unknown number of workers.
M1тАЛ=12,D1тАЛ=20,D2тАЛ=15
Apply Inverse Proportion formula
Since total work remains constant, use the formula M1тАЛ├ЧD1тАЛ=M2тАЛ├ЧD2тАЛ.
12├Ч20=M2тАЛ├Ч15
Calculate unknown value
Solve for M2тАЛ by dividing the total work by the new number of days: M2тАЛ=15240тАЛ.
M2тАЛ=16
B is correct because the calculation M2тАЛ=1512├Ч20тАЛ yields 16 workers.
This concept of inverse proportionality is identical to the Pipe and Cistern problems where rate of flow is inversely proportional to time taken to fill a tank.
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