Question

A factory requires $42$ 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

Finding the number of machines's:

Let the number of machines required be $x$.

Days	$63$	$54$
Machines	$42$	$x$

The number of machines and the number of days are inversely proportional.

Therefore, in inverse proportionality property we have,

$$\begin{gathered} \Rightarrow 63\times 42=54\times \mathrm{x} \\ \Rightarrow \mathrm{x}=\frac{63\times 42}{54} \\ \Rightarrow \mathrm{x}=49 \end{gathered}$$

Hence, $49$ machines will be required to produce the same number of articles in $54$ days.