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PS question - OG13 Q151

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PS question - OG13 Q151

by beavis » Tue Mar 25, 2014 6:54 am
Hi,

I am troubling to understand what this question is really about. Maybe it is because I am not a native English speaker or just it is confusing. Please help me out.

So I understand the total loaded by both the day and night crews will be 8/5 =1 + (3/4)*(4/5). And now the question is 'what fraction of all the boxes loaded by the two crews did the day crew load' I thought this would be simple 2* (8/5). Why is this 5/8?

Can anyone of you explain to me step by step? I really appreciate your time. Thank you.
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by GMATGuruNY » Tue Mar 25, 2014 7:57 am
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

(A) 1/2

(B) 2/5

(C) 3/5

(D) 4/5

(E) 5/8
Day crew:
Let the number of workers = 5.
Let the number of boxes loaded by each worker = 4.
Total number of boxes loaded = 5*4 = 20.

Night crew:
Since the night crew has 4/5 as many workers as the day crew, the number of workers on the night crew = (4/5)5 = 4.
Since each worker on the night crew loads 3/4 as many boxes as each worker on the day crew, the number of boxes loaded by each night crew worker = (3/4)4 = 3.
Total number of boxes loaded = 4*3 = 12.

(Boxes loaded by the day crew)/(Total number of boxes loaded by the two crews) = 20/(20+12) = 20/32 = 5/8.

The correct answer is E.
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