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

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
A group of 5 equally efficient skilled workers together take 18 hours  [#permalink]

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21 Oct 2018, 23:18
00:00

Difficulty:

25% (medium)

Question Stats:

81% (01:46) correct 19% (01:22) wrong based on 32 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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21 Oct 2018, 23:31
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.

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A group of 5 equally efficient skilled workers together take 18 hours &nbs [#permalink] 21 Oct 2018, 23:31
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