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

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Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 139
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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23 Sep 2011, 00:35
4
9
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:57) correct 28% (02:04) wrong based on 474 sessions

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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.
Intern
Joined: 26 Jul 2011
Posts: 21
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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23 Sep 2011, 01:01
4
3
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.
##### General Discussion
Manager
Joined: 14 Mar 2011
Posts: 192
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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23 Sep 2011, 00:56
2
1
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

Manager
Joined: 20 Aug 2011
Posts: 128
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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23 Sep 2011, 01:04
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

Paul= 0.33/0.2=1.65
Abdul=0.25/2=1.25

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

Closest option is 12/47

B
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Manager
Status: Retaking next month
Affiliations: None
Joined: 05 Mar 2011
Posts: 139
Location: India
Concentration: Marketing, Entrepreneurship
GMAT 1: 570 Q42 V27
GPA: 3.01
WE: Sales (Manufacturing)
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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23 Sep 2011, 01:10
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.
Director
Joined: 01 Feb 2011
Posts: 654
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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25 Sep 2011, 09:29
1
1
In this approach we consider the work as some unit of work = 1

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.

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.
Intern
Joined: 24 Sep 2011
Posts: 7
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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25 Sep 2011, 09:50
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

Manager
Joined: 03 May 2014
Posts: 158
Location: India
WE: Sales (Mutual Funds and Brokerage)
Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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20 Mar 2016, 02:37
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

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

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

Total work done X Adams's rate of work

60/47X1/5=12/47
Manager
Joined: 24 Oct 2013
Posts: 134
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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27 Sep 2016, 01:16
[1/5]/[1/3+1/4+1/5] = 60 / (5*47) = 12/47 is the answer
Manager
Joined: 22 May 2015
Posts: 108
Re: Working at their respective constant rates, Paul, Abdul and Adam alone  [#permalink]

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16 Aug 2017, 07:46
1
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]

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15 Oct 2018, 17:06
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Re: Working at their respective constant rates, Paul, Abdul and Adam alone   [#permalink] 15 Oct 2018, 17:06
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