futureguy2020 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 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


OA is E. Please explain the fast way to solve this problem?

I think the fast way is to plug in some nice numbers.
Since the two pieces of information regarding the night shift are related to the information regarding the day shift, let's assign some nice values to the day shift.

Number of workers
Day shift: 5 workers (this is an easy number to find 4/5 of)
Night shift: 4 workers (4/5 of 5 = 4)

Boxes loaded per worker
Day shift: 4 boxes per worker
Night shift: 3 boxes per worker (3/4 of 4 = 3)

Total boxes loaded
Day shift: 5 workers times 4 boxes per worker = 20 boxes
Night shift: 4 workers times 3 boxes per worker = 12 boxes

Combined total boxes for both shifts = 20 + 12 = 32

Of the 32 boxes, the day shift loaded 20 of them.
20/32 = 5/8