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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