A factory requires 42 machines to produce a given number of articles in 56 days.

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.

 

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