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# If 50 apprentices can finish a job in 4 hours, and 30

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Intern
Joined: 22 Oct 2012
Posts: 7
If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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23 Nov 2012, 06:21
3
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15% (low)

Question Stats:

84% (03:14) correct 16% (03:12) wrong based on 240 sessions

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If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121
[Reveal] Spoiler: OA

Last edited by Bunuel on 18 Jul 2013, 11:32, edited 2 times in total.
Renamed the topic, edited the question and the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 44412
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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23 Nov 2012, 06:36
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cv3t3l1na wrote:
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121

50 apprentices can finish the job in 4 hours, thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.

30 journeymen can finish the same job in 4,5 hours, thus:
15 journeymen can finish the job in 4.5*2 = 9 hours;
In 1 hour 15 journeymen can finish 1/9 of the job.

Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/9=29/180 of the job.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.
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Director
Joined: 21 Dec 2009
Posts: 573
Concentration: Entrepreneurship, Finance
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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23 Nov 2012, 06:59
If 50a do the work in 4hr => 10a do same work in 20hr (a = apprentice)
If 30j do the work in 4.5hr => 15j do same work in 9hr (j = journeymen)

For 10a and 15j: 1/20 + 1/9 = 1/t (t = time for this group to finish in 1hr)
t = 180/29hr
if the group can finish 1 unit of the work in 180/29hr
fraction of work in 1hr = time spent / Total time expected to finish
= 1/(180/29) = 29/180
OA is
[Reveal] Spoiler:
B

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Manager
Joined: 26 Dec 2011
Posts: 110
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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30 Nov 2012, 07:11
Apprentice: 50*r1*4 = w...r1 = w/200
Journeyman: 30*r2*4.5 = w...r2 = w/4.5*30

10(A) + 15 (J)==> 10(w/200) + 15(w/4.5*30)===>29W/180
Intern
Joined: 29 Oct 2012
Posts: 38
Location: United States
GMAT 1: 710 Q42 V45
GPA: 3.67
WE: Project Management (Non-Profit and Government)
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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30 Nov 2012, 09:25
I said B, like the posters above for the same reason... but the OA is marked as D... Did I get it wrong? Can someone explain?

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 44412
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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30 Nov 2012, 09:29
gracerx wrote:
I said B, like the posters above for the same reason... but the OA is marked as D... Did I get it wrong? Can someone explain?

Thanks!

OA must be wrong. Correct answer for this question is B.
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Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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24 Jul 2013, 05:42
Bunuel wrote:
cv3t3l1na wrote:
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121

50 apprentices can finish the job in 4 hours, thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.

30 journeymen can finish the same job in 4,5 hours, thus:
15 journeymen can finish the job in 4.5*2 = 9 hours;
In 1 hour 15 journeymen can finish 1/9 of the job.

Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/9=29/180 of the job.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.

Hi Bunnel,

Sorry for the silly question
Logically i could understand this Question and Answer but could u plz explain bit with Formula
Give me more examples for this type.

RRSNATHAN.
Math Expert
Joined: 02 Sep 2009
Posts: 44412
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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24 Jul 2013, 08:42
rrsnathan wrote:
Bunuel wrote:
cv3t3l1na wrote:
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121

50 apprentices can finish the job in 4 hours, thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.

30 journeymen can finish the same job in 4,5 hours, thus:
15 journeymen can finish the job in 4.5*2 = 9 hours;
In 1 hour 15 journeymen can finish 1/9 of the job.

Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/9=29/180 of the job.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.

Hi Bunnel,

Sorry for the silly question
Logically i could understand this Question and Answer but could u plz explain bit with Formula
Give me more examples for this type.

RRSNATHAN.

Don't know what formula approach are you looking for but I can help with theory and practice questions:

DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
PS work/rate problems to practice: search.php?search_id=tag&tag_id=66
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Manager
Joined: 26 Feb 2013
Posts: 168
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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27 Sep 2013, 11:36
rrsnathan wrote:
Bunuel wrote:
cv3t3l1na wrote:
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121

50 apprentices can finish the job in 4 hours, thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.

30 journeymen can finish the same job in 4,5 hours, thus:
15 journeymen can finish the job in 4.5*2 = 9 hours;
In 1 hour 15 journeymen can finish 1/9 of the job.

Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/9=29/180 of the job.

Also, please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3: the name of the topic (subject field) MUST be the first 40 characters (~the first two sentences) of the question.

Hi Bunnel,

Sorry for the silly question
Logically i could understand this Question and Answer but could u plz explain bit with Formula
Give me more examples for this type.

RRSNATHAN.

RRSNATHAN, a little more verbose would be:

50 apprentices in their rate "r" finish 1 job in 4 hours
50r * 4 = 1 => 200r = 1 => r = 10/200 = 1/20
so the rate of 1 apprentice is 1/20

30 journeymen in their rate "j" can finish 1 job in 4.5 hours
30j * 4.5 = 1 => 135j = 1 => j = 15/135 = 1/9

Working together in their respective rates apprentices and journeymen:
1/20 + 1/9 = 29/180
The result is job/hour i.e. in 1 hour which is what the question asks.
SVP
Joined: 08 Jul 2010
Posts: 2017
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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21 Jul 2015, 22:48
cv3t3l1na wrote:
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121

CONCEPT: $$\frac{(Machine_Power * Time)}{Work} = Constant$$

i.e. $$\frac{(M_1 * T_1)}{W_1} = \frac{(M_2 * T_2)}{W_2}$$

Let, Work = W
Apprentice = A
Journeyman = J

i.e. $$\frac{(50A * 4)}{W} = \frac{(30J * 4.5)}{W}$$

i.e. 20A = 13.5J

i.e. 10 apprentices and 15 journeymen = 10A + 15J = 13.5J/2 + 15J = 21.75J

Now, $$\frac{(21.75J * 1)}{W_1} = \frac{(30J * 4.5)}{W}$$

i.e. $$W_1 = 21.75J*W/30*4.5J = 29*W/180$$

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Senior Manager
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Posts: 298
Concentration: Finance
GPA: 3.5
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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21 Jul 2015, 23:35
1
KUDOS
Apprentices: 50 * 4 = 200 job-hours. 1 apprentice's job-hour = 1/200.

Journeymen: 30 * 4.5 = 135 job-hours. 1 journeymen's job-hour = 1/135.

Job done by (10 apprentices + 15 journeymen) = 10/200 + 15/135 = 1/20 + 1/9 = 29/180. Ans (B).
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Director
Joined: 07 Dec 2014
Posts: 929
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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12 Oct 2016, 15:27
If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 4,5 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?

A. 1/9
B. 29/180
C. 26/143
D. 1/5
E. 39/121

a rate=1/(50*4)=1/200
j rate=1/(30*4.5)=1/135
10(1/200)+15(1/135)=29/180
B.
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Posts: 6535
Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]

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26 Nov 2017, 04:35
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Re: If 50 apprentices can finish a job in 4 hours, and 30   [#permalink] 26 Nov 2017, 04:35
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