If 7 maids with 7 mops cleaned 7 floors in 7 hours, how long would it take 3 maids to mop 3 floors with 3 mops?
(a)$\frac{7}{3}$ hours
(b)3 hours
(c)$\frac{49}{3}$ hours
(d)7 hours
Answer
Answer (as printed): D
Explanation
Since each maid would work with one mop, so we shall consider 1 maid and 1 mop as 1 unit. Let the required time be $x$ hours. Less maids and mops, More time (Indirect Proportion) Less floors, Less time (Direct Proportion) Maids \& Mops $\left.\begin{array}{l}3: 7 \\ 7: 3\end{array}\right\}:: 7:: x$ $$\therefore 3 \times 7 \times x=7 \times 3 \times 7 \Leftrightarrow x=\frac{7 \times 3 \times 7}{3 \times 7}=7 .$$
Explanation as extracted from the printed page; notation may be imperfect.