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

Question: The age of the father ten years ago was thrice the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?Solution:Let,son's age 10 years ago be x years. Then, father’s age 10 years ago = 3x years.Son's present age = (x + 10) years Father's present age = (3x + 10) years.according to the question,(3x + 10) + 10 = 2 (x + 10 + 10)⇒ 3x + 20 = 2 (x + 20) ⇒ 3x + 20 = 2x + 40 ∴ x = 20Ratio of present ages of father and the son = (3x + 10)/(x + 10)= {(3 × 20) + 10}/(20 + 10)= 70/30 = 7 : 3