The age of the father 10 years ago was thrice the age of his son. Ten years hence, the father's age will be twice that of his son. What is the ratio of their present ages?

Ten years ago, the father’s age was three times the son’s age.

Ten years hence, the father’s age will be twice the son’s age.

Let the present ages of the father and son be F and S respectively.

According to the question;

Ten years ago, the father’s age was three times the son’s age:

F - 10 = 3(S - 10)

F−10 = 3S−30

F = 3S – 20………….(1)

Ten years hence, the father’s age will be twice the son’s age:

F + 10 = 2(S + 10)

F + 10 = 2S + 20

F = 2S + 10……………….(2)

From equations (1) and (2):

3S - 20 = 2S + 10

S = 30

Substituting S = 30 into equation (1):

F = 3(30) - 20 = 90 - 20 = 70

​$$\text{Ratio of father's age to son's age} = \frac{F}{S} = \frac{70}{30} = \frac{7}{3}$$​​

Thus, The ratio of their present ages is 7 : 3.