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Machine A can do a job in 24 hours at a constant rate and machine A do

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Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post Updated on: 13 Mar 2016, 06:10
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Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


* A solution will be posted in two days.

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Originally posted by MathRevolution on 11 Mar 2016, 06:04.
Last edited by MathRevolution on 13 Mar 2016, 06:10, edited 3 times in total.
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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 11 Mar 2016, 06:35
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate and machine A do the job in 8 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


* A solution will be posted in two days.

Hi,

The Q does not seem to be properly framed..
I believe it should be--

Machine A can do a job in 24 hours at a constant rate and machine A does the job alone for 8 hours. Machine B can do the same job at a 2/3 constant rate of machine A. If machine B does the rest job, what is the amount of hours done by machine B alone?


solution


machine A will do 8/24 in 8 hrs, so A does 1/3 of the work ..
Therefore, B will do the remaining 2/3 rd work alone..
As the speed of B is 2/3 rate of A, B will do the 2/3rd work in same time that A takes to complete full job...
ans 24
C

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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 13 Mar 2016, 06:11
Sorry for the confusion. I have revised the question.
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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 13 Mar 2016, 22:16
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


Power of Machine A=W/24hrs. Since Machine A does the job for 8 hours, which becomes (W/3)/8hrs and 2W/3 is left. However, as power of Machine B is 2/3 of Machine A, power of B is (2/3)(W/24hrs)=(2W/3)/24hrs. Eventually, it takes 24 hours for Machine B to do the rest of the job.
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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 13 Mar 2016, 22:24
1
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


* A solution will be posted in two days.

In 8 hours A can complete one third work. The remaining work is two thirds.
B performs two third of the efficiency of A; So B takes 36 hours to complete the full task.
Now B has to do only two thirds of the work. Therefore, two thirds of 36 hours = 24 hours.
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Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 13 Mar 2016, 22:44
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


* A solution will be posted in two days.

We can equate work done as follows:
8/24 + x/36 = 1

x/36=2/3
x=24 hrs
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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 25 Aug 2017, 09:05
Ans c 24 hours
Given
A takes 24 hours
And

The machine b is 2/3 as consistent as a

So time taken by it would be 3/2 as A

A works for 8 hours so 8/24 = 1/3 work is done

Remaining work = 1-1/3= 2/3

A completed 1/3 of work in 8 hours and b would take 3/2 as time as A so
A would complete the same work in 3/2*8= 12 hours

So 1/3 of work is completed by b in 12 hours
So 2/3 will be done in 24 hours

Hope it helps
Peace


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Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 26 Aug 2017, 12:40
1
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs

* A solution will be posted in two days.

A's rate = \(\frac{1}{24}\)

B's rate is \(\frac{2}{3}\) (of) A:

\(\frac{1}{24}\) * \(\frac{2}{3}\) = \(\frac{1}{36}\) = B's rate

Amount of work for B? A works for 8 hours. \((\frac{1}{24})\) * 8 = \(\frac{1}{3}\) of the work is finished.

1 - \(\frac{1}{3}\) = \(\frac{2}{3}\) of work remains.

Time for B to finish? B has to finish remaining \(\frac{2}{3}\) of work. At B's rate, W/r = t, that will take

\(\frac{\frac{2}{3}}{\frac{1}{36}}\) =

\(\frac{2}{3}\) * 36 = 24 hours

Answer C
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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 27 Aug 2017, 21:09
Since Machine A does a job in 24 hours,
lets assume the number of units of work done to be a multiple of 24(for eg, 72 units)
So the rate of Machine A doing the work is 3 units/day

It has been given that B does the work at \(\frac{2}{3}\)rd the rate of A.
Therefore Machine B does the work at the rate of 2 units/day

Since Machine A does the work for 8 hours,
Machine B does the rest of the work for x days till the work is complete.

8*3 + x*2 = 72(total units of work)
2x = 48
x = 24
Therefore, Machine B takes 24 hours to complete the remaining work(Option C)
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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 31 Aug 2017, 10:22
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


The rate of machine A is 1/24, so in 8 hours 1/3 of the job is completed, and thus 2/3 of the job is left to be completed.

If the rate of machine B is 2/3 that of machine A, then the rate of machine B is (2/3)(1/24) = 1/36.

Thus, it will take machine B (2/3)/(1/36) = 2/3 x 36 = 24 hours to complete the rest of the job.

Answer: C
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Re: Machine A can do a job in 24 hours at a constant rate and machine A do [#permalink]

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New post 31 Aug 2017, 13:07
MathRevolution wrote:
Machine A can do a job in 24 hours at a constant rate. If Machine A does the job for 8 hours and Machine B does the rest of the job, which works at 2/3 constant rate of Machine A. How long will it take for Machine B alone to do the rest of the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 28hrs
E. 32hrs


B's time=(3/2)*24=36 hours
(2/3 job)/(1/36 rate)=24 hours
C
Re: Machine A can do a job in 24 hours at a constant rate and machine A do   [#permalink] 31 Aug 2017, 13:07
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