Frankly speaking I don't have any idea about how to calculate/know the age of a raga. During the invent of music raagas were known as "jati". Later towards 5th century AD during saint Matanga's period it got the name raga.Earlier there were only 18 ragas. Later more ragas were discovered. There are 72 janaka ragas and lots of janya ragas to each of these janaka ragas. Janaka ragas number is finite, but janya ragas number is infinite. Some janaka ragas are ancient whereas others are recent. And some janya ragas are very ancient, for example, Gowla, Vasantha, Saurashtram, Madyamavathi, Kedaragowla, Neelambari, etc. Raga Vivardhini, Ranjini and Navarasa Kanada are innovations of Sri Thyagarajaswami, which was sometime during 19th century. Janaka raga Manjari was published in 1952. Dr. Balamuralikrishna created ragas like Ganapathi, Sarvashri, Mahati, Lavangi etc., so these are very recent ragas.
Joyesh, apart from these limited knowledge I'm not sure whether any method to know the age