After nearly 200 years of existence, the persian empire was conquered by which ruler, who controlled most of the western world in the 300s bc?

Alexander the Great.

Explanation:

The Persian Empire, which was formed during the 6th century BCE was a series of dynasties that lasted into the 20th century in areas of what is now Iran (most current day Iranians consider themselves descendants of this long lasting empire).  

Alexander the Great, was the formidable conqueror of the ancient world and King of Macedonia. Amongst his historical exploits, and following in his father´s campaigns, he managed to conquer, in the 4th century BCE, the powerful Persian Empire, demonstrating his military skills and his thirst for conquest.  

i thinl it is the 1st answer