In a family, the sum of the present ages of the father, mother and the only son is x years. After yyears, the sum of their ages will be : 

Correct option is D

​Let’s solve this step by step:

- The family consists of a father, mother, and one son.
- The sum of their present ages is (x) years.
- We need to find the sum of their ages after (y) years.

Step 1: Understand the present ages
The present ages of the father, mother, and son sum to (x):

​$$\text{Father's age} + \text{Mother's age} + \text{Son's age} = x$$​

There are 3 family members.
Step 2: Calculate their ages after (y) years
After (y) years:
- The father’s age increases by (y)years.
- The mother’s age increases by (y) years.
- The son’s age increases by (y) years.

Each person’s age increases by \(y\), and since there are 3 people, the total increase in their ages is:
y + y + y = 3y


 Step 3: Find the new sum of their ages
The sum of their ages after (y) years is the present sum plus the total increase:
x + 3y

 Step 4: Match with the options
The result (x + 3y) corresponds to option (D).

Answer: (D) (x + 3y) years