Let p represent the number of people originally in the fort. Then the quantity of provisions is 90p (person-days). The scenario can be described by
90p = 20p +50(p+600)
90p = 70p +30000 . . . . . . . eliminate parentheses
20p = 30000 . . . . . . . . . . . . subtract 70p
p = 1500 . . . . . . . . . . . . . . . . divide by 100
There were originally 1500 people in the fort.