Question

A factory required 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days?

Answer 1

Let the number of machines required to produce articles in 54 days be x. 
The following table is obtained.

Number of machines	42	x
Number of days	63	54

More the number of machines, lesser will be the number of days that it will take to produce the given number of articles. 
Thus, this is a case of inverse proportion. 
Therefore, 
\(42 × 63 = 54× x\)
\(x=\frac{42 × 63 }{ 54}\)
\(=49\)
Hence, the required number of machines to produce the given number of articles in 54 days is 49.