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Question on combined work rates

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by Uva@90 » Mon Aug 26, 2013 7:20 pm
stephkhaira wrote:Each of 10 machines works at the same constant rate. Together they complete a job in 16 hours. How many hous does it take 8 machines to finish the job?

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[spoiler]ans: 20[/spoiler]
Hi Stephkhaira,
Given: 10 machine takes 16 hours to complete a certain job.
To Find: How many hour does it take to complete same job using 8 machines.

Note: For these kind of problem we need to imagine some value( for example, here each machine produce one unit per hour)

Solution:
Ok, Let's imagine each machine produce One unit per hour.
therefore, 10*1*16=160.
So 10 machines produce 160 units of total in 16 hours.

Let X be no of hours for 8 machines to produce 160 Units.
In the same rate,
8*1*X =160

Hence X = 20

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Uva.
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by [email protected] » Mon Aug 26, 2013 9:32 pm
Hi stephkhaira,

Uva has explained a great, straight-forward approach to this question (it's the same way that I would solve this problem), so it's worth knowing.

As an aside, there's also a "ratio pattern" that's worth knowing:

You'll notice that in this question, the number of machines drops from 10 to 8; this is a 20% decrease. To end up with the same total output (in this case, the completed job), the way to offset the 20% decrease in machines is with a 25% increase in the other variable (in this case, the number of hours).

We start with 16 hours per machine; increasing this by 25% = 16 + 4 = 20 hours per machine.

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by vinay1983 » Wed Aug 28, 2013 6:47 am
I usually use the proportion method.

10 machines take 16 hours, 8 machines will take?

Notice that the no. of machines required for completion of the work have reduced, hence the no. of hours required will be more(Inverse proportion)

Machines time in hours

10 16


8 x

I.e x/16=10/8

x= 10/8*16=20

Hope this helps!
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by ganeshrkamath » Wed Aug 28, 2013 10:21 am
stephkhaira wrote:Each of 10 machines works at the same constant rate. Together they complete a job in 16 hours. How many hous does it take 8 machines to finish the job?

18
20
22
24
26

[spoiler]ans: 20[/spoiler]
Let each machine take M hours to complete the work alone.
Rate of each machine = 1/M per hour
Rate of 10 machines = 10/M per hour
So the machines take M/10 hours to complete the work = 16 hours
M = 160

So 8 machines can finish the job in M/8 = 160/8 = 20 hours

Choose B

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