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At a loading dock

by alex.gellatly » Sun Sep 02, 2012 8:01 pm
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 day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

1/2
2/5
3/5
4/5
5/8

Thanks
A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231
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by adthedaddy » Sun Sep 02, 2012 10:27 pm
Refer this post: https://www.beatthegmat.com/og-problem-138-t25203.html

Multiple ways to solve this problem are indicated.
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by GMATGuruNY » Mon Sep 03, 2012 5:17 pm
alex.gellatly wrote: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 day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

1/2
2/5
3/5
4/5
5/8

Thanks
Plug in SMALL numbers.

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 loaded 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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by Anurag@Gurome » Mon Sep 03, 2012 7:44 pm
alex.gellatly wrote: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 day crew, what fraction of all the boxes loaded by the two crews did the day crew load?

1/2
2/5
3/5
4/5
5/8

Thanks
Say, number of workers in the day crew = w
=> Number of workers in the night crew = 4w/5.

Say, total number of boxes loaded by the day crew = x
=> Number of boxes loaded by each of the workers in the day crew = x/w.
=> Number of boxes loaded by each of the workers in the night crew = (3/4)*(x/w).
=> Total number of boxes loaded by the night crew = Number of workers in the night crew * Boxes loaded by each of the workers in the night crew = (4w/5)*[(3/4)*(x/w)] = 3x/5.

Therefore, total number of boxes loaded by the two crews = Boxes loaded by the day crew + Boxes loaded by the night crew = x + 3x/5 = 8x/5.

Therefore, required fraction = Boxes loaded by the day crew/Total number of boxes loaded by the two crews = x/(8x/5) = [spoiler]5/8[/spoiler].

The correct answer is E.
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