Explanation:

- The Hathigumpha inscription by King Kharavela details his reign and achievements.

- It states that in the eleventh year of his reign, Kharavela faced a confederacy of Tamil States termed "Tramiradesa Sanghatam."

- This confederacy had existed for 165 years before Kharavela's eleventh year.

- 165 years before Kharavela's eleventh year translates to the confederacy being 113 years old at that time.

Based on the information, Option 4: 113 years old is the correct answer.