OG question

GaneshMalkar 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?

Let us assume, number of workers in the day crew = w
Hence, Number of workers in the night crew = 4w/5.

Also assume that the total number of boxes loaded by the day crew = x
So, 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) = 5/8.

The correct answer is E.

GaneshMalkar 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 - E

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 = E

Cheers,
Brent