Let the polulation a year ago be x
So, x+ 30x/100 = 338000 [30% increase means x + 30x/100]
130x/100= 338000
X = 338000 x 100/ 130
X= 260000
Let y be the polulation 2 years back
Y + 30y/100 = 260000
130y/100 = 260000
Y = 260000 x 100/ 130
Y= 200000
population of the city 2 years ago = 200000