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1. 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. $7 hours$

Solution:

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 floor, Less time (Direct proportion)

\begin{matrix} Maids &  Mops 3 : 7 \\ Floors 7 : 3 \end{matrix}} :: 7 : x

\begin{aligned} ∴ 3 \times 7 \times x = 7 \times 3 \times 7 \\ \Leftrightarrow x = \frac{(7 \times 3 \times 7)}{(3 \times 7)} \\ \Leftrightarrow x = 7 \end{aligned}

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