Question

A mans age is 3 times the sum of ages of his 2 sons one of him is twice old as other .
in four years the sum of sons age will be half of fathers age find ages of all three

Answer 1

Let sum of younger son be x years.
Therefore, age of elder son = 2x years
Father's age, as per question = 3(2x+x) = 9x years

Younger son's age in 4 years = (x+4) years
Elder son's age in 4 years = (2x+4) years
Father's age in 4 years = (9x+4) years

As per question however,
Half of father's age = Sum of sons' ages
Therefore,
=> (9x+4)/2 = (x+4)+(2x+4)
=> 9x+4 = 2(3x+8)
=> 9x+4 = 6x+16
=> 3x = 12
=> x = 4

So before 4 years,
Younger son's age = x = 4 years
Elder son's age = 2x = 8 years
Father's age = 9x = 36 years

Answer 2

yes this is the only correct answer