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# If a group of 5 craftsmen takes 3 hours to finish a job

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Joined: 21 Jun 2014
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If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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10 Mar 2017, 22:40
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5% (low)

Question Stats:

86% (01:03) correct 14% (01:54) wrong based on 98 sessions

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If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job

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Re: If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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11 Mar 2017, 00:13
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HKD1710 wrote:
If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job

I figured D.

1- An apprentice works at 2/3 the rate of a craftsman.

5 craftsmen finish work in 3 hours.
--> 1 craftsman does the job in $$= 5x3 = 15h$$
--> 1 apprentice = 2/3 craftsman
--> time by 1 apprentice will hence be reciprocal $$=15 x 3/2 = 45/2 = 22.5$$
--> time by 4 apprentices $$= 22.5/4 = 5.625$$

1 is -- clearly sufficient.

2- I kind of figured there is just one variable unknown which is the time taken by apprentices alone. We have rate of work of craftsmen and craftsmen + apprentices combined. One variable can be easily found. I actually found this question on a quick search, solved a few years ago.

https://gmatclub.com/forum/work-word-pr ... ml#p843620
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Re: If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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21 Feb 2020, 12:04
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Joined: 02 Sep 2009
Posts: 64242
Re: If a group of 5 craftsmen takes 3 hours to finish a job  [#permalink]

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24 Feb 2020, 00:40
HKD1710 wrote:
If a group of 5 craftsmen takes 3 hours to finish a job, how long will it take a group of 4 apprentices to do the same job?

(1) An apprentice works at 2/3 the rate of a craftsman.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job

Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

$$time*speed=distance$$ <--> $$time*rate=job \ done$$.

So, if we say that the rate of a craftsmen is $$x$$ job/hours and the rate of an apprentice is $$y$$ job/hour then we'll have $$(5x)*3=job=(4y)*t$$ --> $$(5x)*3=(4y)*t$$. Question: $$t=\frac{15x}{4y}=?$$

(1) Each apprentice works at 2/3 the rate of a craftsman --> $$y=\frac{2}{3}x$$ --> $$\frac{x}{y}=\frac{3}{2}$$ --> $$t=\frac{15x}{4y}=\frac{45}{8}$$ hours. Sufficient.

(2) The 5 craftsmen and the 4 apprentices working together will take 45/23 hours to finish the job --> as the 5 craftsmen need 3 hours to do the job then in 45/23 hours they'll complete (45/23)/3=15/23 rd of the job (15 parts out of 23) so the rest of the job, or 1-15/23=8/23 (8 parts out of 23) is done by the 4 apprentices in the same amount of time (45/23 hours): $$\frac{5x}{4y}=\frac{15}{8}$$ --> $$\frac{x}{y}=\frac{3}{2}$$, the same info as above. Sufficient.

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Re: If a group of 5 craftsmen takes 3 hours to finish a job   [#permalink] 24 Feb 2020, 00:40