Aside from potential capitalization in the third sentence, all three are correct under specific situations The boy became a king at the age of 10. - The boy became a king of an unspecified region. The boy became king at the age of 10. - It would be understood which region is being discussed. The boy became king of this region. The boy became the King at the age of 10. The boy became the king at the age of 10. - Again, the region would already be established prior to this sentence. He would most likely be the currently reigning king, or he was the king for a specific time period being discussed.