Let the present age of father and son be represented by '2x' years and 'x' years respectively, where x is a positive integer.
According to the problem, the present age of father and son has a ratio of 2:1. Therefore, we can write:
present age of father / present age of son = 2/1
2x / x = 2/1
Simplifying this equation, we get:
2x = 2 * x
Hence, the present age of father is 2x years and the present age of son is x years.
After 20 years, the age of the father will be (2x + 20) years and the age of the son will be (x + 20) years.
According to the problem, the father will be two third greater aged than the son. Therefore, we can write:
age of father after 20 years = (2/3) * age of son after 20 years + age of son after 20 years
2x + 20 = (2/3)(x + 20) + x + 20
Simplifying this equation, we get:
2x + 20 = (2/3)x + (40/3)
Multiplying both sides by 3, we get:
6x + 60 = 2x + 120
Subtracting 2x from both sides, we get:
4x + 60 = 120
Subtracting 60 from both sides, we get:
4x = 60
Dividing both sides by 4, we get:
x = 15
Hence, the present age of the father is 30 years (2x) and the present age of the son is 15 years (x).
Therefore, the present age of the father and son are 30 years and 15 years respectively.