Ranjit was born and raised in Mumbai in a family with a theatre background, where he received his early education at Campion School, Mumbai, and started his acting career. His father is from a Gujjar background, while his mother, Pearl Padamsee, was of partial Jewish descent on her mother's side, but remained Christian during her life. He made his film debut in Basu Chatterjee's "Khatta Meetha", following which he played prominent parts in Bollywood comedy classics such as Basu Chatterjee's "Baton Baton Mein" (1979) and Hrishikesh Mukherjee's "Khubsoorat" (1980). Thereafter, he moved to the United States 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.