Given that, 42 machines are required to produce a given number of articles in 63 days.
Let the required number of machines be x.
We can see that if the number of machines is increased then less number of days would be required to produce the same number of articles.Thus, the two quantities are in inverse proportion.So we have:
\(\Rightarrow x_1y_1 = x_2y_2\)
\(\Rightarrow 42 \times 63 = x \times 54\)
\(\Rightarrow x = 49\)
Hence, the required number of machines is 49.