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Working at their respective constant rates, Paul, Abdul and Adam alone

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Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47

Innovative Solutions will be highly Appreciated.
[Reveal] Spoiler: OA

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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GMATPASSION wrote:
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47



Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.

adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work

>( 60/47 *12)/60 =12/47

Answer B

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 23 Sep 2011, 02:01
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We can solve the problem just by calculating the work done in 1 hr.

Work done by adam in 1 hr is 1/5.
total work done by all three in 1 hr is (1/3 + 1/4 +1/5) = 47/60

so, fraction of work done by Adam = (1/5)/(47/60) = 12/47.

Option B.

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 23 Sep 2011, 02:04
Work is measured in job per unit time.
Let j be job

Rate of work done by
Paul= J/3= 0.33J
Abdul= J/4= 0.25J
Adam=J/5=0.2J

Relative rate w.r.t Adam
Paul= 0.33/0.2=1.65
Abdul=0.25/2=1.25
Adam=1

Hence relative proportion of work done= 1.65:1.25:1

Adam's share= 1/(1.65+1.25+1)=1/3.9
Closest option is 12/47

B
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 23 Sep 2011, 02:10
vishal4584 wrote:
We can solve the problem just by calculating the work done in 1 hr.

Work done by adam in 1 hr is 1/5.
total work done by all three in 1 hr is (1/3 + 1/4 +1/5) = 47/60

so, fraction of work done by Adam = (1/5)/(47/60) = 12/47.

Option B.


Your Solution Here seems to be good. But I would like To clarify Some silly doubts:

If all three work together to finish the work, what fraction of the work will be done by Adam-- Question asks us to find :

Ratio of work done by adam/ Work Done by all three .

But you have based ur calculations on only 1 hour. Why is that? Infact, all three take longer than 1 hour to finish the work.

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 25 Sep 2011, 10:29
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In this approach we consider the work as some unit of work = 1

-------Paul----Abdul----Adam

Rate---1/3-----1/4------1/5

when they all work together their combined rate = 1/3+1/4+1/5 = 47/60

time taken by them to finish to unit work = 60/47 hours

work done by adam in 60/47 hours = (60/47)*(1/5) = 12/47

fraction of work done by adam = adam's work / total work = (12/47) / 1 = 12/47

So coming back to your question its 1 unit of work here. thats why the total work they can do= 1. you can consider the work done as some 'w' still the answer would be same.

Answer is B.

GMATPASSION wrote:
vishal4584 wrote:
We can solve the problem just by calculating the work done in 1 hr.

Work done by adam in 1 hr is 1/5.
total work done by all three in 1 hr is (1/3 + 1/4 +1/5) = 47/60

so, fraction of work done by Adam = (1/5)/(47/60) = 12/47.

Option B.


Your Solution Here seems to be good. But I would like To clarify Some silly doubts:

If all three work together to finish the work, what fraction of the work will be done by Adam-- Question asks us to find :

Ratio of work done by adam/ Work Done by all three .

But you have based ur calculations on only 1 hour. Why is that? Infact, all three take longer than 1 hour to finish the work.

Kudos [?]: 146 [1], given: 42

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 25 Sep 2011, 10:50
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47

Step 1: find the individual rates by finding the inverse of the times - Paul: 1/3, Abdul: 1/4, Adam: 1/5
Step 2: add the rates - 1/3 + 1/4 + 1/5 = 47/60
Step 3: the inverse of the combined rate above tells you the time. i.e. takes 60/47 hours to finish the job together
Step 4: apply the 60/47 hours to Adam's rate to find his share of work - W = 1/5*60/47 = 12/47

Answer B.

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 20 Mar 2016, 03:37
GMATPASSION wrote:
Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction of the work will be done by Adam?

(A) 1/4
(B) 12/47
(C) 1/3
(D) 5/12
(E) 20/47

Innovative Solutions will be highly Appreciated.


Rate of work done
Paul 1/3
Abdul 1/4
Adam 1/5

Total rate of work
1/3+1/4+1/5=47/60

Total work done is inverse of total rate of work=60/47

Adams contribution will be

Total work done X Adams's rate of work

60/47X1/5=12/47

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 27 Sep 2016, 02:16
[1/5]/[1/3+1/4+1/5] = 60 / (5*47) = 12/47 is the answer

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Re: Working at their respective constant rates, Paul, Abdul and Adam alone [#permalink]

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New post 16 Aug 2017, 08:46
Say there are 60 units of work to be done.So

Paul takes 3 hrs => in 1 hr he completes 20 units of work
Abdul takes 4 hrs => in 1 hr he completes 15 units of work
Adam takes 5 hrs => in 1 hr he completes 12 units of work

In 1 hour all together can complete 47 units of work. Hence time taken to complete 60 units of work is 60/47 hours.

Now in 60/47 hours Adam completes (12*60)/47 units of work. Hence his contribution would be (12*60)/(47*60) which is 12/47.
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone   [#permalink] 16 Aug 2017, 08:46
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