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time & work problm from Grep - hw do i solve this

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by anjaligeorge1 » Thu Jun 05, 2008 8:21 pm
Each of 10 machines work at the same constant rate doing a certain job.The amount of time needed by he 10 machines , working together , to complete the job is 16 hrs.How many hours would be needed if only 8 of the machines, working together , were used to complete the job

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by kishore » Thu Jun 05, 2008 8:43 pm
Each of 10 machines work at the same constant rate doing a certain job.The amount of time needed by he 10 machines , working together , to complete the job is 16 hrs.How many hours would be needed if only 8 of the machines, working together , were used to complete the job


Answer: 20

More machines less number of hours to complete the Job.

So, Number of Machines and Hours are Inversely proportional

M1 * H1 = M2 * H2

10 * 16 = 8 * H2

=> 8 * H2 = 10 * 16
=> H2 = 10 * 2 = 20
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by AleksandrM » Fri Jun 06, 2008 9:26 am
kishore,

Can you elaborate a little bit. You approach is not completely clear to me. Thanks.
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by aatech » Fri Jun 06, 2008 9:37 am
Each machine performs equally so, no of machine is inversaly proportional to the time take by those machines to finish the work

means m = k/h wheren m = no of machines and h = no of hours and k = constant

when m = 10, h = 16 so 10 = k/16 => k = 160

when m = 8, h = k/m = 160/8 = 20
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by gmataspirant » Fri Jun 06, 2008 12:40 pm
Hi All,

The explaination given by all of you makes sense. I was trying to solve this question by a method learned from Princeton Review but it doesn't seem to work.

10 Machines / 16 hours = 8 Machines/x hours

The answer would be 12.8 but it is clearly wrong.

Could someone please explain me, why this approach is not working for this question ? :oops:
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by Ian Stewart » Fri Jun 06, 2008 1:10 pm
gmataspirant wrote:Hi All,

The explaination given by all of you makes sense. I was trying to solve this question by a method learned from Princeton Review but it doesn't seem to work.

10 Machines / 16 hours = 8 Machines/x hours

The answer would be 12.8 but it is clearly wrong.

Could someone please explain me, why this approach is not working for this question ? :oops:
That ought to be:

10 machines times 16 hours = 8 machines times x hours

This question is similar to other questions that use the (archaic) phrase 'man hours'. I'll use the term 'person hours' instead. If 20 people work together for 30 hours to complete a job, the job requires 20*30 = 600 'person hours' to complete. So if 15 people work on the job instead, they'll need to work together for 40 hours, since 15*40 = 600.

In this question, 10 machines working for 16 hours do 160 hours of machine work. 8 machines would need to do 20 hours each.
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by gmataspirant » Fri Jun 06, 2008 1:18 pm
Thanks Ian,

I just worked the problem. It is no different than what already been said.

Formula:

Amount of Work = Rate X Time

10 Machines Scenario::

As amount of work is not given, let’s assume that Amount of work to be “k”.

k = 10 * 6 = 160

8 Machine Scenario::

From the previous calculation we know the amount of work to be done is 160

160 = 8x
x=20
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