Word problems

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.

Brent@GMATPrepNow wrote:

saidov.mikhail 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

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

thanks for explanation. does it have any sense to try solving this question algebraically?