Ten years ago, a mother was thrice as old as her son. After 10 years, she will be twice as old as her son. What is the ratio of their present ages?

Let present age of son be x

10 years ago son's age was (x-10) and mothers age was 3(x-10)

present age of mother = 3(x-10)+10

after 10 years , mother's age = 3(x-10)+10+10 = 3x-10

                        son's age = x+10

given ,after 10 years mother will be twice as her son 

                   3x-10 = 2(x+10)

                 3x -10 =2x +20

                 3x-2x = 20+10

                 x=30(son's present age)

 mothers present age 3(x-10)+10 = 3x-20

                                                  =$$3\times30$$ - 20

                                                  = 90 -20 

                                                  = 70

ratio of present age of mother and son is 70 : 30 or 7:3