First, let's simplify each expression separately:

20 : 2 2/15 = 20 / (2 * 15 + 2) = 20 / 32 = 5/8

25 5/7 : 1 1/35 = (25 + 5/7) / (1 + 1/35) = (25 + 5/7) / (35/35 + 1/35) = (25 + 5/7) / (36/35) = (175/7 + 5/7) / (36/35) = 180/7 / 36/35 = (180/7) * (35/36) = 25

Now, let's substitute these values into the original expression:

5/8 : 25 : 21 7/9 - 4 2/3 + 1

Now, let's simplify the expression:

5/8 : 25 : 198/9 - 14/3 + 1

5/8 : 25 : 22 - 14/3 + 1

5/8 : 25 : 22 - 14/3 + 3/3

5/8 : 25 : (66 - 14) / 3 + 3/3

5/8 : 25 : 52 / 3 + 3/3

5/8 : 25 : 52 / 3 + 1

5/8 : 25 : 17 1/3

Therefore, the final simplified expression is 5/8 : 25 : 17 1/3