Four gardeners with four grass mowers mow 400 sq. m of ground in 4 hours. How long would it take for eight gardeners with eight grass mowers to mow 800 sq. m of ground?
(a)4 hours
(b)6 hours
(c)8 hours
(d)12 hours
Answer
Answer (as printed): A
Explanation
Since each gardener would work with one grass mower, so we shall consider 1 gardener and 1 grass mower as one unit. Let the required time be $x$ hours. More gardeners and grass mowers, Less time (Indirect Proportion) More area, More time (Direct Proportion) Gardeners \& grass mowers $$\left.\begin{array}{c} 8: 4 \\ 400: 800 \end{array}\right\}:: 4: x \begin{aligned} & \therefore 8 \times 400 \times x=4 \times 800 \times 4 \\ & \Leftrightarrow x=\left(\frac{4 \times 800 \times 4}{8 \times 400}\right)=4 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.