The event of Ghadir took place on the tenth of the hegira year but there are different views about Imam Ali's date of birth. However, if we are to determine the Imam's date of birth, it depends on which report is considered to be stronger and more authentic. Only then one can determine, with relative confidence, the Imam's date of birth. According to a more famous account by historians about Imam Ali's date of birth, he was born on 30th 'Am al-Fil (the year of the elephant) which is ten years before the prophetic mission of the Holy Prophet of Islam, peace be upon him and his descendants.[1] Therefore, Imam Ali (AS) was ten years old when the Holy Prophet (S) was appointed for the prophetic mission. Considering that the Holy Prophet (S) was in Mecca during the first 13 years of the prophetic mission, the event of Ghadir Khum took place ten years after the Prophet (S) migrated to Medina. Hence, on this basis, the Commander of the Faithful, Imam Ali, peace be upon him, was 33 years old on Ghadir Day.
--------------------------------------------------------------------------------
[1] Vide: Kulayni, Muhammad bin Ya'qub, Al-Kafi, vol.1, p. 457, Dar al-Kutub al-Islamiyah, Tehran, fourth edition, 1407 A.H; Arbali, Ali b. Isa, Kashful Ghummah fi Ma'refat al-A'emma, researched and edited by Rasuli, Mahallati, Sayed Hashe, vol.1, p. 82, Bani Hashem Publications, Tabriz, first edition, 1381 A.H; Majlisi, Muhammad Baqir, Behar al-Anwar, vol.35, p. 8, Al-Wafa Institute, Beirut, 1404 AH.
source : islamquest
