2 persons working 2 hours a day assemble 2 machine in 2 days. The number of machines assemble by 6 persons working 6 hours a day in 6 day is ?

Answer: Option D

Let the required number of machine be x
More persons, More machines (Direct proportion)
More working working hours, More machines (Direct proportion)
More days, More machines (Direct proportion)
$$\begin{array}{c}\text{Persons 2}:6\text{hfill}\\ \text{Working hours 2}:6\text{hfill}\\ \text{Days 2}:\text{6}\text{hfill}\end{array}\}::2:x$$
$$\begin{array}{rl}& \therefore 2\times 2\times 2\times x=6\times 6\times 6\times 2\\ & \iff x=\frac{\left(6\times 6\times 6\times 2\right)}{\left(2\times 2\times 2\right)}\\ & \iff x=54\end{array}$$