A farmer had 700 geese and duck altogether. He sold 1/3 of his geese and bought another 20 ducks. Afterthat, the number of ducks was 1/6 of the number of geese. How many more geese and ducks were there at first

Initial condition:

g+d=700

g=700-d

final condition

d+20 = (2g/3) (1/6)

d+20=g/9

9d+180=g, and since g=700-d we can say

9d+180=700-d

10d+180=700

10d=520

d=52, and since g=700-d

g=648

The original number of ducks was 52 and the original amount of geese was 648.

So there were originally (648-52) 596 more geese than ducks.