A father was twelve times as old as his son twenty years back. Now he is twice as old as his son. What are their present ages?

Options

A. Father 44 and son 22
B. Father 55 and son 33
C. Father 66 and son 44
D. None of these

Explanation

To solve the problem, let's denote the present age of the son as \( x \). According to the information given in the question, the present age of the father will then be \( 2x \) since he is currently twice as old as his son.

### Step 1: Set up the equations based on the information provided.
Twenty years ago, the son's age would have been \( x - 20 \) and the father's age would have been \( 2x - 20 \). According to the problem, twenty years ago, the father was twelve times as old as the son. Therefore, we can set up the following equation:

\[ 2x - 20 = 12(x - 20) \]

### Step 2: Expand and simplify the equation.
Now, let's expand the right side of the equation:

\[ 2x - 20 = 12x - 240 \]

Next, we will rearrange the equation to isolate \( x \):

\[ 2x - 20 + 240 = 12x \]

This simplifies to:

\[ 2x + 220 = 12x \]

### Step 3: Solve for \( x \).
Now, we will move \( 2x \) to the right side of the equation:

\[ 220 = 12x - 2x \]

This simplifies to:

\[ 220 = 10x \]

Now, divide both sides by 10:

\[ x = 22 \]

### Step 4: Find the present ages.
Now that we have the present age of the son, we can find the present age of the father:

\[ \text{Father's age} = 2x = 2 \times 22 = 44 \]

### Conclusion:
The present ages are:
- Son: 22 years
- Father: 44 years