Workers at loading dock. Need a strategy! PS#138

[BlueDragon2010]

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

I'm not sure of the best way to approach this question. Any ideas?

[Patrick_GMATFix]

The question is mis-categorized. It should be posted in the Problem solving section

This is PS 138 from the Official Guide 12. As many ratio questions that do not limit you to any specific real amounts, this question can be solved by plugging in values that agree with the ratio. In fact, the easiest values to plug in are the values that are part of the ratios provided. Have a look at the detailed solution to see what I mean.

The OA to this is E

The solution hinted above as well as two alternative solutions and a take away lesson are available in the attached document. If you cannot see the attachment get it here.

Hope that helps.
-Patrick

[albatross86]

If each day worker loaded 4 boxes, then each night worker loaded 3 boxes.
Let's say there are 5 day workers, and thus 4 night workers

(This is just plugging in numbers that satisfy the ratios provided i.e. 3/4 and 4/5)

So day workers loaded 5*4 = 20 boxes and night workers loaded 3*4 = 12 boxes. TOTAL = 20+12 = 32

What fraction was loaded by the day crew? = 20/32 = 5/8

Pick E.

[selango]

Let the number of boxes each worker on day crew loaded be B

-->Number of boxes each worker on night crew loaded is 3/4B

Let the number of day crew worker be N

-->Number of night crew worker 4/5N

Number of boxes by night crew workers=3/4B*4/5N=3/5*BN

Number of boxes by day crew workers=B*N=BN


fraction of boxes loaded by day crew workers=BN/(BN+3/5*BN)=5/8