Question

A factory requires 42 machines to produce a given number of articles in 63 days.
Find the number of machines required to produce the same number of articles in 54 days.

Answer 1

Let the required number of machines be denoted by 'n' and number of days taken be 'd'.

As number of machines increases, the number of days required to make articles decreases, hence they are inversely proportional.

$n\times d$ = constant
$n_1\times d_1$ = $n_2\times d_2$

Using inverse proportion condition,

$\frac{42}{n}$ = $\frac{54}{63}$

$n=\frac{42\times 63}{54}$

n = 49

So, 49 machines are required.