Question

A factory requires 42 machines to produce a given number of articles in 56 days. How many machines would be required to produce the same number of articles in 48 days?

Answer 1

Let x be the number of machines required to produce same number of articles in 48.
Then, we have:

No. of machines	42	x
No. of days	56	48

Clearly, less number of days will require more number of machines.
So, it is a case of inverse proportion.
$$\begin{gathered} \mathrm{Now},42\times 56=x\times 48 \\ \Rightarrow x=\frac{42\times 56}{48} \\ \Rightarrow x=49 \end{gathered}$$

Therefore, 49 machines would be required to produce the same number of articles in 48 days.