The ratio of the ages of two persons is 4 : 7 and the age

The ratio of the ages of two persons is 4 : 7 and the age of one of them is greater than that of the other by 30 years. The sum of their ages (in years) is

Ages of the persons = 4x and 7x years.
∴ 7x – 4x = 30 ⇒ 3x = 30
⇒ x = 10
∴ Sum of their ages = 4x + 7x
= 11x years
= 11 × 10 = 110 years