6 machines can do a job in 8 hrs.

5 machines con do a job in ?

Now think, will 5 machines take more than 8 hrs, or less? Of course more than 8 hrs since fewer machines are working.

So number of hours 5 machines will take = \(8 * (\frac{6}{5})\)

Basically, you need hours so given hours term i.e. \(8 * \frac{6 machines}{5 machines}\) to get 9.6 hours.

We multiply by 6/5 to increase 8 since more hours are required.

It is actually a Variation question (Inverse Variation here) but it is just easier to think in terms of more/less.

Another e.g. 10 people make 5 chairs in a day. How many people do we need to make 12 chairs.

Simply multiply 10 (the number that you want to change) by 12/5 because you want to increase the number of people to make more chairs: \(10 * (\frac{12}{5}) = 24\) people

Yet another e.g. 10 people need 4 hours to complete a job. How many hours do 18 people need to complete the same job?

\(4 * (\frac{10}{18})\) = 2.2 hrs

If there are more people, they will need fewer hours so multiply by 10/18 (not 18/10).

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