I'd start by recognizing that the smaller triangle, at the top, is similar to the larger (whole) triangle.
Then:
a b
------- = ---------
15+a 20+b
Then 20a + ab = 15b + ab. Subtract ab from both sides. We then get 20a = 15b. Note also that
40 b
----- = ----------
60 b+20
so that 40b + 800 = 60b, or 800 = 20b, or b = 40.
If b = 40, then we can find a from the relationship 20a = 15b found earlier. With b=40, 20a = 15(40) = 600, so a = 30
a = 30
b= 40