The sum of present ages of a father and his son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What will be the age of the father after 4 years?

Let present age of the father, mother and son be x, y and z respectively
Sum of present ages of father and son = (Mother's present age + 8 years)
⇒ x + z = y + 8 years ...(i)
Mother's present age = (Son's present age + 22)
⇒ y = z + 22 years ...(ii)
Put the value of y in equation (i) we get
x + z = z + 22 + 8
⇒ x + z = z + 30
⇒ x = 30 years
∴ Father's present age = 30 years
Age of the father after four years = 30 + 4 = 34 years
∴ Required age of father
= 34 years.
Answer: 34 years.