\(\frac{m_1d_1h_1}{w_1}=\frac{m_2d_2h_2}{w_2}\), whereas w = machines

\(\frac{2*2*2}{2}=\frac{6*6*6}{x}\)

\(x=\frac{6*6*6}{2*2}=6*9=54\)

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

Work=Rate·Time
Time (hours): 2 hours·2 shifts of two hours·2 cause two people putting in the work=8
Work (machines): 2

Rate
one person produces \(\frac{2 machines}{8 hours}=\frac{0.25 machines}{hour}\)

Work=Rate·Time
Work=\(\frac{0.25 machines}{1 hour}·(6 persons·6 hours·6 shifts) hours\)
Work=\(\frac{(0.25 machines·6^3 hour)}{1 hour}\)
Work=\((0.25 machines·6^3)\)
Work=\((0.25 machines·216)\)
Work=54 machines

Given: 2 persons working 2 hours a day assemble 2 machines in 2 days.
Asked: The number of machines assembled by 6 persons working 6 hours a day in 6 days is

1 person working 1 hours a day in 1 day will assemble = 2/2*2*2 = 1/4 machines
The number of machines assembled by 6 persons working 6 hours a day in 6 days = 6*6*6/4 = 54

IMO D
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