One year ago, the ratio of the age (in years) ofA to that of B was4 : 3. The ratio of their respective ages, 3 years from now,will be 6 : 5. What will be the ratio of respective ages of A and B, 9 years from now?

One year ago, the ratio of the age (in years) of A to that of B = 4 : 3
After 3 year, the ratio of the age (in years) of A to that of B = 6 : 5
After 3 year, let the age of A and B are 6x and 5x.
ATQ,
$$\frac{4x + 4}{3x + 4} = \frac{6}{5}$$
20x + 20 = 18x + 24
2x = 4
x = 2
After 9 year, the ratio of the age (in years) of A to that of B = 6x + 6 : 5x + 6 
6 $$\times$$ 2 + 6 : 5 $$\times$$ 2 + 6 = 18 : 16 = 9 : 8