He was educated at government schools in Sydney's south-eastern suburbs, including Kensington Public School in Kensington, where he was dux after repeating his final year in 1935, and Sydney Boys High School from 1936–40 in nearby Moore Park, graduating with A levels in English, Mathematics, and Chemistry and B levels in Physics and French. After completing his secondary education, in 1941, Murphy matriculated to the University of Sydney, though he had not been successful in gaining a university scholarship awarded to the top 100 in the state. His initial scholastic performance was ordinary and he briefly considered transferring to study a Bachelor of Arts majoring in psychology at the Faculty of Arts. Murphy excelled in his final year, graduating from the School of Chemistry, Faculty of Science with a Bachelor of Science with Honours in Organic Chemistry. In 1943, he commenced working in the chemical industry, thereby coming under the authority of the wartime Manpower Directorate.