To solve for x in the equation 3/20 : 10/33 = 19 4/5 : x - 15, we will first convert the mixed numbers to improper fractions.

3/20 : 10/33 can be simplified as 3/20 : 10/33

19 4/5 is equivalent to 99/5 as an improper fraction. Therefore, our equation can also be written as 99/5 : x - 15

Now, we can cross multiply to solve for x:

(3/20) (x - 15) = (10/33) (99/5)

(3x/20 - 45/20) = (990/165)

Multiplying both sides by 20 to get rid of the fractions, we get:

3x - 45 = 1200

Add 45 to both sides to isolate x:

3x = 1245

Divide by 3 to solve for x:

x = 415

Therefore, the value of x in the equation 3/20 : 10/33 = 19 4/5 : x - 15 is 415.