Vijayadashami is observed for different reasons and celebrated differently in various parts of the Indian subcontinent.In the southern, eastern, northeastern, and some northern states of India, Vijayadashami marks the end of Durga Puja, remembering goddess Durga's victory over the buffalo demon Mahishasura to restore and protect dharma.In the northern, central and western states, the festival is synonymously called Dussehra (also spelled Dasara, Dashahara). In these regions, it marks the end of "Ramlila" and remembers god Rama's victory over the Ravan. On the very same occasion, Arjuna alone decimated more than 1,000,000 soldiers and defeated all Kuru warriors including Bhishma, Drona, Ashwatthama, Karna and Kripa, a significant example of victory of good (Dharma) over evil (Adharma).
Ramayana - (Lord Rama) happened before Mahabharata (Lord Krishna) both being avatars of Lord Vishnu.
So how both the events taking place on the same day?
Killing Demon Ravana by Lord Rama & Arjun defeating great warriors on the same day.
Note : Vijayadashami festival celebration dates are different every year.
Did Arjuna defeated the mighty warriors in a different era (Mahabharata) with different dates and not on the same day?