Let the number of adult be x and children be y, then
x+y=80.........(1) (total number of people)
Also
2x+y/3=85 (given one adult eats 2 plate noodle and 3 children eat 1 plate noodle. So one child eat 1/3 plate noodle. Also given total plates of noodle is 85)
that is
6x+y=255........(2)
Solve (1) and (2)
(2)-(1) implies
5x=175
x=35
So the number of adult is 35. From equation (1)
y=80-x=80-35=45
So there are 35 adults and 45 children.