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

The more the number of machines, the less 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

⇒ `63/54 = x/42`

⇒ `x = (42xx63)/54`

⇒ x = 49

Hence, the required number of machines to produce the given number of articles in 54 days is 49.