The ratio of the present ages of a son and his father is 2 : 5 and that of his father and mother is 3 : 2. After 6 years the ratio of the age of the son to that of his mother becomes 7 : 11. What is the present age of the father?

Solution

Let the present age of the son and father be 2x and 5x respectively. Also, Ratio of present ages of father and mother = 3 : 2 So, let the present age of father and mother be 3y and 2y respectively. Since father's age is common, 5x = 3y Now, take father's age as 15a . Therefore, Present age of son = 6a Present age of father = 15a Present age of mother = 10a After 6 years, Age of son = 6a + 6 Age of mother = 10a + 6 According to the question, {6a + 6}/{10a + 6} = {7/11} 11(6a + 6) = 7(10a + 6) 66a + 66 = 70a + 42 70a - 66a = 66 - 42 4a = 24 a = 6 Therefore, present age of father: 15a = 15 x 6 = 90