Fraction Algebra

[EMAN]

I'm having a problem setting up part of this problem:



At a loading dock, each worker on a 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 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

[2010gmat]

Lets say day crew has 100 workers
therefore night crew has 4/5 of 100 = 80 workers

say each day crew worker lifted 4 boxes .. total boxes loaded by day crew = 100*4 = 400

therefore each night crew lifted = 3/4 of 4 = 3 boxes
total no. of boxes loaded by night crew = 80*3 = 240

fraction of day/total = 400/(400+240) = 5/8

E

[xcusemeplz2009]

IMO E

let day crew no. be X and and load per worker is y;total=xy

night crew worker (4/5)x and load (3/4)y;tot = (3/5)xy

grand tot=8/5xy

day fraction=xy/(8/5)xy=5/8

OA pls

[EMAN]

Great use of smart numbers. E is correct.

[vivek.kapoor83]

ACC to me also
Ans should be E

Shift Worker Box Total
Day 5 4 20
Night 4 3 12

Ratio 20/32 = 5/8 wht is the source...?

[EMAN]

OG 12 in the Problem Solving Section is the source. Good work.

[scholardream]

Total night crew / Total day crew = 3/4 * 4/5 = 3/5
-> Total day crew / Total 2 crew = 1 / (1+3/5) = 5/8
-> E