In a family, the father's age is 5 times the age of one of his sons. Mother's age is 4 times the age of their other son. Difference in the parents' ages is half the sum of the sons' ages. Then:

Father's age = 5× (age of Son 1)

Mother's age = 4× (age of Son 2)

Difference in parents' ages = $$\frac{1}{2}$$​ ​× (sum of the sons' ages).

Let the ages of the two sons be x and y. Then:

Father's age = 5x

Mother's age = 4y

From the given condition:

Difference in parents' ages:

5x - 4y = $$\frac{1}{2}(x + y)$$​​

2(5x - 4y) = x + y

10x - 8y = x + y

10x - x = 8y + y

9x = 9y  ⟹  x = y

Since x = y,

Thus, the two sons are of the same age(twins)