I believe the origin in English comes from the word "due" meaning to owe something. Being "on duty" probably means paying what is owed, in this case the person owes his time/work for the specified purpose - hence, being "on duty".
I believe the origin in English comes from the word "due" meaning to owe something. Being "on duty" probably means paying what is owed, in this case the person owes his time/work for the specified purpose - hence, being "on duty".