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If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]
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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]
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23 Nov 2012, 06:36
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: rulesforpostingpleasereadthisbeforeposting133935.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]
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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
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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



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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!



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



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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. Answer: B. Also, please read and follow: rulesforpostingpleasereadthisbeforeposting133935.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]
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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. Answer: B. Also, please read and follow: rulesforpostingpleasereadthisbeforeposting133935.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: workwordproblemsmadeeasy87357.htmlDS work/rate problems to practice: search.php?search_id=tag&tag_id=46PS 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]
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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. Answer: B. Also, please read and follow: rulesforpostingpleasereadthisbeforeposting133935.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]
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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. \(W_1 = 21.75J*W/30*4.5J = 29*W/180\) Answer: option B
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Re: If 50 apprentices can finish a job in 4 hours, and 30 [#permalink]
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21 Jul 2015, 23:35
Apprentices: 50 * 4 = 200 jobhours. 1 apprentice's jobhour = 1/200. Journeymen: 30 * 4.5 = 135 jobhours. 1 journeymen's jobhour = 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]
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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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