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A group of 5 equally efficient skilled workers together take 18 hours

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A group of 5 equally efficient skilled workers together take 18 hours  [#permalink]

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New post 22 Oct 2018, 00:18
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  25% (medium)

Question Stats:

82% (01:43) correct 18% (01:52) wrong based on 109 sessions

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A group of 5 equally efficient skilled workers together take 18 hours to finish a job. How long will it take for a group of 4 skilled workers and 3 apprentices to do the same job, if each skilled worker works at an identical rate and each apprentice works at an identical rate?

(1) An apprentice works at 2/3 the rate of a skilled worker.
(2) 6 apprentices and 5 skilled workers take 10 hours to complete the same job.

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A group of 5 equally efficient skilled workers together take 18 hours  [#permalink]

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New post 22 Oct 2018, 00:31
From the question:

5 equally skilled workers take 18 hours. So, individually 1 takes 18*5 hours or 90 hours.

From S1:
Apprentice work = \(\frac{2}{3}(90)\) = 60 hours.
\(4S+3A = \frac{4}{90}+\frac{3}{60} = \frac{8+9}{180} = \frac{180}{17}\) hours.
Sufficient.

From S2:
\(\frac{6}{A} + \frac{1}{18} = \frac{1}{10}\)

Solving gives A as \(\frac{90}{4}*\frac{1}{6} = \frac{15}{4}\) hours for 1 Apprentice.
Form this we can calculate the time for 4S+3A.
Sufficient.

D is the answer.
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Re: A group of 5 equally efficient skilled workers together take 18 hours  [#permalink]

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New post 01 Jan 2019, 04:24
Afc0892 wrote:
From the question:

5 equally skilled workers take 18 hours. So, individually 1 takes 18*5 hours or 90 hours.

From S1:
Apprentice work = \(\frac{2}{3}(90)\) = 60 hours.
\(4S+3A = \frac{4}{90}+\frac{3}{60} = \frac{8+9}{180} = \frac{180}{17}\) hours.
Sufficient.

From S2:
\(\frac{6}{A} + \frac{1}{18} = \frac{1}{10}\)

Solving gives A as \(\frac{90}{4}*\frac{1}{6} = \frac{15}{4}\) hours for 1 Apprentice.
Form this we can calculate the time for 4S+3A.
Sufficient.

D is the answer.

Hey, Afc0892 !

First of all, I love your posts mate! Second, I have to point out a little, silly mistake in your calc. in st (2). It is sufficient, and your thinking is great, buuuuuut it's not 15/4 for A! it should yield the same 60 hours as pointed out by you in st (1).

Have great NY!

Best, gota900
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Re: A group of 5 equally efficient skilled workers together take 18 hours   [#permalink] 01 Jan 2019, 04:24
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