Explanation:

Let the age of father be x years and sum of the ages of his children by y years.

After 5 years,

Father's age = (x + 5) years

Sum of ages of his children = (y + 10) years

From the given information, we have:

x = 3y ...(1)

and x + 5 = 2(y + 10)

 x - 2y = 15 ...(2)

From (1) and (2), we have,

3y - 2y = 15 

 y = 15

Hence, option 1 is the correct answer.