Problem Solving

Q--> At a loading dock each worker on the night crew loaded ¾ 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) ½
(B) 2/5
© 3/5
(D) 4/5
(E) 5/8

IMO E

There is a quick way of solving this:
Let the number of day workers be equal to 100%=1
Let the number of boxes each day worker loads be equal to 100%=1
So the number of boxes loaded by the day worker crew is 1*1=1

Now the number of night workers is 3/4 of the number of day workers and the number of boxes each night worker can load equals 4/5 of the boxes each day worker can load.
So the number of boxes loaded by the night worker crew is 3/4*4/5=3/5

The total number of boxes loaded by the two crews is 1+3/5=8/5
The fraction of the total boxes that are loaded by the day crew is 1/8/5=5/8

Of course, you can also solve this problem by picking numbers, whatever serves you best.

Day workers are the standard so lets say each day worker loaded and there was 1 worker - day work:1

Night workers: each worker loaded 3/4 and there were 4/5 of workers, night work: 3/4*4/5=3/5
Total work: 1+3/5=5/5+3/5=8/5
Out of which day did 5/5 so they did (5/5)/(8/5)=5/8
It's E.