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

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cv3t3l1na
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If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  Updated on: 18 Jul 2013, 11:32
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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
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Originally posted by cv3t3l1na on 23 Nov 2012, 06:21.
Last edited by Bunuel on 18 Jul 2013, 11:32, edited 2 times in total.
Renamed the topic, edited the question and the OA.
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  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.

Answer: B.

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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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  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
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  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
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  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!
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  30 Nov 2012, 09:29
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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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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  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.

Answer: B.

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.

Thankz in advance,
RRSNATHAN.
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  24 Jul 2013, 08:42
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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.

Answer: B.

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.

Thankz in advance,
RRSNATHAN.


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

Theory on work/rate problems: work-word-problems-made-easy-87357.html

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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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  27 Sep 2013, 11:36
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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.

Answer: B.

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.

Thankz in advance,
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.
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  21 Jul 2015, 22:48
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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


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. \(W_1 = 21.75J*W/30*4.5J = 29*W/180\)

Answer: option B
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  21 Jul 2015, 23:35
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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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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  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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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  25 Mar 2021, 14:36
can anyone please explain what's wrong here?

50 apprentices take 4 hours.. so each hour they would complete 50/4 =25/2 of the job.

each apprentice would do 1/50 × 25/2 = 1/4 of the job.

but the actual rate of each apprentice is 1/20.

i'm unable to grasp my mistake. Bunuel VeritasKarishma please help

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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  26 Mar 2021, 02:06
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Reply to pavanbatra,
True in both cases , yet the 1/4 of the job completed per hour is when 50 apprentices work , and 1/20 of the job completed in one hour is when only 10 apprentices work. I hope it makes sense.
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink] New post  26 Mar 2021, 02:31
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pavanbatra wrote:
can anyone please explain what's wrong here?

50 apprentices take 4 hours.. so each hour they would complete 50/4 =25/2 of the job.

each apprentice would do 1/50 × 25/2 = 1/4 of the job.

but the actual rate of each apprentice is 1/20.

i'm unable to grasp my mistake. Bunuel VeritasKarishma please help

Posted from my mobile device


50 apprentices take 4 hours.. so each hour they would complete 50/4 =25/2 of the job.

This is not correct. They need to complete 1 job. They complete it in 4 hrs. It means, every hour 50 apprentices work together to complete 1/4th of the job.

50 apprentices complete 1/4th of the job every hour
So 10 apprentices must be doing (1/4)/5 = 1/20th of the job every hour

Note what is meant by 25/2 of the job. This is equal to 12.5 of the job i.e. 12.5 times the initial job.
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