Question

If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?

Answer 1

Hint: In the first step find the time taken by 1 machine to make 5 widgets. Now, apply the unitary method to find the time taken by 1 machine to make 1 widget. Multiply this time obtained with 100 to determine the time that 1 machine will take to make 100 widgets. Find divide the obtained expression to get the time that 100 machines will take to make 100 widgets.

Complete step by step answer:
Here, we have been provided with the time that is taken by 5 machines to make 5 widgets and we are asked to determine the time taken by 100 machines to make 100 widgets. So, let us use the basic approach of the unitary method to get the answer.
$$\because$$ Time taken by 5 machines to make 5 widgets = 5 minutes.
Now, since 5 machines are taking 5 minutes therefore 1 machine will take five times the time taken by 5 machines to make the same number of widgets. So, we have,
$$\Rightarrow$$ Time taken by 1 machine to make 5 widgets = 25 minutes.
Applying the unitary method to find the time taken by 1 machine to make 1 widget, we get,
$$\Rightarrow$$ Time taken by 1 machine to make 1 widget = $${\displaystyle \frac{25}{5}}=$$ 5 minutes.
Now, we have found the data for 1 machine and 1 widget, so let us consider the data for 100 machines and 100 widgets. Since, 1 machine takes 5 minutes to make 1 widget, therefore to make 100 widgets the same single machine will take 100 times more time. So, we have,
$$\Rightarrow$$ Time taken by 1 machine to make 100 widgets = $$5\times 100=500$$ minutes
Applying the unitary method to find the time taken by 100 machines to make 100 widgets, we get,
$$\Rightarrow$$ Time taken by 100 machines to make 100 widgets = $${\displaystyle \frac{500}{100}}=$$ 5 minutes.Hence, our answer is 5 minutes.

Note:
 One may make a mistake by observing the pattern of data given and would conclude that the required time would be 100 minutes. But this will be a totally wrong approach and answer. We have to apply the basic unitary method to get the answer. Note that if we will consider the same number of machines and widgets then the required time will always be 5 minutes.