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

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

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New post 10 Mar 2017, 23:40
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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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New post 11 Mar 2017, 01:13
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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 &nbs [#permalink] 11 Mar 2017, 01:13
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