If $x$ men, working $x$ hours per day, can do $x$ units of work in $x$ days, then $y$ men, working $y$ hours per day would be able to complete how many units of work in $y$ days?
(a)$\frac{x^{2}}{y^{3}}$
(b)$\frac{x^{3}}{y^{2}}$
(c)$\frac{y^{2}}{x^{3}}$
(d)$\frac{y^{3}}{x^{2}}$
Answer
Answer (as printed): D
Explanation
Let the required number of units of work be $z$. More men, More work (Direct Proportion). More working hours, More work (Direct Proportion). More days, More work (Direct Proportion). Men $x:y$, Hours per day $x:y$, Days $x:y$ :: $x:z$. $\therefore (x \times x \times x \times z) = (y \times y \times y \times x) \Leftrightarrow z = \frac{y^{3}}{x^{2}}$.
Explanation as extracted from the printed page; notation may be imperfect.