Ok, one of the most important thing about ratios is remembering to adapt them for use in equations.

From the information given, we can see that

a/b = 1/3 (1)

AND

(a+210)/(b-210) = 3/2 (2)

We can use these simultaneous equations to solve for each quantity. NOTE that the quantities A and B are the quantities BEFORE the exchange of liquid.

From Eq.1:

a = b/3 (1')

Sub (1') into (2):

(b/3+210)/(b-210) = 3/2

2(b/3+210) = 3(b-210)

2b/3 + 420 = 3b - 630

7/3b = 1050

b = 450

Hence,a = 150