After 20 new students joined the class at the start of the school year, the number of students increased to 160+20 = <<160+20=180>>180
However, at the end of the year, 1/3*180 = <<1/3*180=60>>60 students had transferred from the school.
The total number of students remaining in the school at the end of the year is 180-60 = <<180-60=120>>120
#### 120