i don't know what OG11 is, but when i read this question, i think it helps to plug in numbers.

day crew = 100 people
night crew = 4/5d = 80 people

day crew rate = 4 boxes
night crew rate = 3/4d = 3 boxes

100 day crew people * 4 boxes = 400 boxes
80 night crew people * 3 boxes = 240 boxes

day / total = day / day + night = 400 / (400+240) = 5 / 8 = answer E.

Alternatively, you can solve it this way.
Consider they hardly loaded any box. Also ignore 4/5 person. (Just take it for calculation)

Day Crew: 1 Person loaded 1 box.
Night Crew: 4/5 Person loaded 3/4 box.

Total Boxes loaded by Day crew = 1*1 = 1
Total Boxes loaded by Night crew = (4/5)*(3/4) = (3/5)
Grand total of boxes loaded = 1 + (3/5) = 8/5

Boxes by Day Crew / Total boxes loaded = 1 / (8/5)

= 5/8.

--E

Thanks!!!!

I prefer algebraic way of doing it:

Day crew --> x*n (x boxes, n persons)
Night crew --> 3x/4 * 4n/5 (3/4 (x) boxes, 4/5(n) persons) = 3/5 (x*n)
Total --> 8/5 (x*n)
Day crew frachtion = x*n / (8/5 * (x*n)) == 5/8 Hence E.