Problem: If x men working x hours a day for each of x days produce x articles, then the number of articles (not necessarily an integer) produced by y men working y hours a day for each of y days is:
Answer Choices:
A. y2x3
B. x2y3
C. y3x2
D. x3y2
E. y
Solution:
Since x men working x2 hours produce x articles, one man, working x2 hours, produces one article. Therefore, one man produces x21 part of one article in one hour.
Let n be the number of articles produced by y men working y hours a day for each of y days.
Then n=y⋅y⋅y⋅x21=x2y3
or
T=MDHA where T is the time required for 1 article, A, the number of articles, M, the number of men, D, the number of days, H, the number of hours per day. T=x⋅x⋅xx=x21
∴A′=TM′D′H′=x21⋅y⋅y⋅y=x2y3