Five years ago, the ratio of the ages of A and B was 3 4. Five years from now,the ratio of their ages will be 4 : 5. What is the ratio of A and B, 10 years from now?

Let the ages of A and B are 3p and 4p five years ago respectively

                                     A                         B

5 years ago               3p                        4p

After 5 years           3p+10                 4p+10

After 10 years         3p+15                 4p+15

Given ratio of ages of A and B after 5 years is 4:5

$$=$$>        $$\ \frac{\ 3p+10}{4p+10}=\ \frac{\ 4}{5}$$

      $$\ \ 15p+50=\ 16p+40$$

                       $$p=10$$

Therefore ratio of ages of A and B after 10 years = 3p+15: 4p+15                    

                                        = 3(10)+15 : 4(10)+15        

                                        = 45:55              

                                        = 9:11