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?
Solution:
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.
Now, $42 \times 56=x \times 48$
$\Rightarrow x=\frac{42 \times 56}{48}$
$\Rightarrow x=49$
Therefore, 49 machines would be required to produce the same number of articles in 48 days.