Why is the verb accompanied the word percentage both appear in plural and singular?
What percentage of visitors come from the United States?
What percentage of visitors comes from the three countries in East Asia?

Question

Why is the verb accompanied the word percentage both appear in plural and singular?
What percentage of visitors come from the United States? 
What percentage of visitors comes from the three countries in East Asia?

Answer

Natives use both, but most teachers and editors prefer to use plural verbs for percentages of countable things.  For percentages of uncountable things, you HAVE TO use singular verbs.
OK: what percentage of the people was happy?
Better: What percentage of the people were happy? [remember that "people" is the plural of "person"]
Required: What percentage of the cake was eaten?