A father is 7 times as old as his son. Two years ago, the father was 13 times as old as his son. Father’s present age is

Options

A. 24 years
B. 28 years
C. 30 years
D. 32 years

Answer

To solve the problem, we need to find the present age of the father given the conditions about his age and his son's age.

### Step-by-Step Solution:

1. **Define Variables:**
Let the present age of the son be \( x \) years. Then, the present age of the father will be \( 7x \) years (since the father is 7 times as old as his son).

2. **Set Up the Equation for Two Years Ago:**
Two years ago, the son's age would be \( x - 2 \) years, and the father's age would be \( 7x - 2 \) years. According to the problem, two years ago, the father was 13 times as old as his son. Therefore, we can set up the equation:
\[ 7x - 2 = 13(x - 2) \]

3. **Expand the Equation:**
Now, we will expand the right side of the equation:
\[ 7x - 2 = 13x - 26 \]

4. **Rearrange the Equation:**
To isolate \( x \), we can rearrange the equation:
\[ 7x - 13x = -26 + 2 \]
\[ -6x = -24 \]

5. **Solve for \( x \):**
Dividing both sides by -6 gives us:
\[ x = \frac{-24}{-6} = 4 \]

6. **Find the Father's Present Age:**
Now that we have the son's present age \( x = 4 \), we can find the father's present age:
\[ \text{Father's age} = 7x = 7 \times 4 = 28 \text{ years} \]

### Final Answer:
The father's present age is **28 years**.

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