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

If the articles are to be produced in lesser number of days, more machines are required.

Hence, the number of machines and number of articles are in inverse proportion.

Let the number of machines required to make the articles in $54$ days be $a$

Then, $42:a::$ inverse ratio of $63:54$
$=>42:a=54:63$

Applying the rule, product of extremes $=$ product of means

$42\times 63=a\times 54$

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

$a=49$
Hence, $49$ machines are required to make the articles in $54$ days.