Can someone show me how he/she would approach this?

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?

1/2
2/5
3/5
4/5
5/8

This problem is an excellent candidate for 'smart numbers,' because all of the quantities in the problem are indeterminate (only ratios are given).

The easiest - and arguably the best - smart numbers here are exactly the numbers IN the ratios:
Night crew = 4 workers, day crew = 5 workers
Each night worker loads 3 boxes, each day worker loads 4 boxes

So:
The day crew loads 5 x 4 = 20 boxes
The night crew loads 4 x 3 = 12 boxes
The day crew loaded 20/32 = 5/8 of all the boxes.

If you are hurried and have to guess, notice that it's plain that the day crew loads more than half of the boxes (because there are more of them in the first place, and each of them loads more boxes). This makes the first two answer choices ridiculous.