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If 12 machines can produce 600 items in 5 days, how many items can 8 machines produce in 10 days?
800
750
900
600
800
Use the proportionality rule: Output is directly proportional to (Machines ├Ч Days). Items = k├ЧM├ЧD. Calculate k=600/(12├Ч5)=10, then simply calculate 10├Ч8├Ч10.
12 machines produce 600 items in 5 days. We need to find the output of 8 machines in 10 days.
W1тАЛM1тАЛ├ЧD1тАЛтАЛ=W2тАЛM2тАЛ├ЧD2тАЛтАЛ
Use the proportionality rule: Output is directly proportional to (Machines ├Ч Days). Items = k├ЧM├ЧD. Calculate k=600/(12├Ч5)=10, then simply calculate 10├Ч8├Ч10.
Students often multiply all three values together or flip the denominator and numerator, failing to keep the Work (W) in the denominator.
Define variables
Identify the given values: M1тАЛ=12, D1тАЛ=5, W1тАЛ=600 and M2тАЛ=8, D2тАЛ=10, W2тАЛ=?.
M1тАЛ=12,D1тАЛ=5,W1тАЛ=600,M2тАЛ=8,D2тАЛ=10,W2тАЛ=x
Set up the equation
Substitute the known values into the work-time formula to express the relationship.
60012├Ч5тАЛ=x8├Ч10тАЛ
Calculate the unknown work
Solve for x by cross-multiplying: 60/600=80/x, which simplifies to 1/10=80/x, so x=800.
x=6080├Ч600тАЛ=800
A is correct because the calculated production is 800 items based on the direct proportionality of machine-days to output.
This concept is foundational for Pipe and Cistern problems and Chain Rule questions in Quantitative Aptitude sections.
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