His father Krishnamachari was an engineer who was involved in the construction of the Napier Bridge and the General Hospital, Madras while his uncle, S. Gopalachari was a distinguished lawyer who served as Diwan of Travancore.
At the encouragement of two European surgeons Nibblock and Gifford, Rangachari joined the Madras Medical College in 1900 graduating in 1904.
Rangachari joined the government service as an Assistant Surgeon in 1906 and served in Egmore, Hyderabad, Mayavaram, Tanjore, Negapatam, Kumbakonam and Berhampore.
In July 1917, Rangachari was made the Deputy Superintendent of the Egmore Women's and Children's Hospital, the first Indian to hold the post.
In 1919, he became surgeon and served till 1922, when he quit government service to set up private practice at Kensington Nursing Home on Poonamallee High Road.