The present age of a father is 4 years more than double the age of his son. After 10 years, the father's age is 30 years more than his son. Then the present age of father is:

The correct option is 56 years.

Let us break down the problem step-by-step to find the present age of the father.

Step 1: Define the variables for their present ages.
Let the present age of the son be represented by $S$ years.
Let the present age of the father be represented by $F$ years.

Step 2: Translate the first condition into an equation.
The problem states: "The present age of a father is 4 years more than double the age of his son."
Mathematically, this can be written as:

$$F=2S+4$$

Let this be Equation (1).

Step 3: Translate the second condition into an equation.
The problem states: "After 10 years, the father's age is 30 years more than his son."
After 10 years:
The father's age will be $F+10$ years.
The son's age will be $S+10$ years.
According to the condition:

$$F+10=(S+10)+30$$

We can simplify this equation by subtracting 10 from both sides:

$$F=S+30$$

Let this be Equation (2). (Note: This indicates that the age difference between the father and the son is always 30 years.)

Step 4: Solve the equations to find the son's present age.
Since both equations express $F$ in terms of $S$, we can set them equal to each other:

$$2S+4=S+30$$

Subtract $S$ from both sides:

$$S+4=30$$

Subtract 4 from both sides:

$$S=26$$

So, the present age of the son is 26 years.

Step 5: Calculate the present age of the father.
Substitute the value of $S=26$ into Equation (2):

$$F=26+30$$

$$F=56$$

Thus, the present age of the father is 56 years.