Either your question is worded incorrecttly or you left out a piece of information.
If 1/5 drive , then 4/5 do not drive.
3/8 of non driving use bikes so 5/8 of non driving use public transportation.
Of, when talking about fractions or percents means multiplication so,
5/8 * 4/5 = 1/2. So 1/2 the workers don't drive and use public transportation. But since you don't know how many people work for the company, you cannot answer your question. Let's say your company had 40 employees. That would mean 20 fit the category your looking at.