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05 Nov 2010, 13:47
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (02:00) correct
21%
(02:15)
wrong
based on 823
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If 6 machines run at the same constant rate, they can complete a job in 8 hours. If only 5 of these machines run at this rate, how many more minutes will be required to complete the same job?
A. 38
B. 72
C. 80
D. 90
E. 96
A. 38
B. 72
C. 80
D. 90
E. 96
06 Nov 2010, 05:44
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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).
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).
15 Jan 2011, 08:01
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Bookmarks
a simpler way to tackling such questions is to convert the information into man-hours or, in this case, machine-hours.
6 machines in 8 hours = 6*8= 48 machine-hours
5 machines will take = 48/5= 9.6 hrs
so 1.6hrs more or \(\frac{8}{5}\) hrs = \(\frac{8*60}{5} mins = 96mins\)
HTH
