Ranjit was born and brought up in Mumbai in a family with theatre background, where he recieved his early education at Campion School, Mumbai and started his acting career. He made his debut with Basu Chatterjee's Khatta Meetha , following with he played prominent parts in the Bollywood comedy classics such as Basu Chatterjee's Baton Baton Mein (1979) and Hrishikesh Mukherjee's,Khubsoorat (1980). Thereafter, he moved to the USA in the early 1980s. He wrote the screenplay and acted in Sam & Me (directed by Deepa Mehta) which won an Honorable Mention at Cannes in 1991.
His mother, Pearl Padamsee, was well-known theatre personality, drama teacher and actress on stage and film. His stepfather, Alyque Padamsee is an advertising maven and directs and acts in plays.