10 years from now, A you will be twice as old as B. 5 years ago, A was three times as old as B. What are the present ages of A and B?

A = 50 and B = 20

Explanation:

Call A and B the 2 present ages.

Ten years from now, A is twice as old as B - ->

(A + 10) = 2 (B + 10) (1)

Five years ago, A was 3 times as old as B - ->

(A - 5) = 3 (B - 5) (2).

Solve the system (1) and (2).

From (2) - -> A = 3B - 15 + 5 = 3B - 10.

Replace this value of A into (1) - ->

3B - 10 + 10 = 2B + 20 - -> B = 20. Then,

A = 3B - 10 = 60 - 10 = 50.

Check

!0 years from now - -> A = 60 and B = 30 - -> A = 2B. OK

5 years ago - -> A = 45 and B = 15 - -> A = 3B. OK