A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 52 years now, then the son's age 8 years back was

Options

A. 10 years
B. 18 years
C. 12 years
D. 20 years

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the statement
The father states, "I was as old as you are at present at the time of your birth." This means that the father's age at the time of the son's birth was equal to the son's current age.

### Step 2: Define the variables
Let the son's current age be \( x \). The father's current age is given as 52 years.

### Step 3: Set up the equation
Since the father was as old as the son is now at the time of the son's birth, we can express this mathematically:
- The father's age at the time of the son's birth = Father's current age - Son's current age = \( 52 - x \)
- According to the father's statement, this age equals the son's current age:
\[ 52 - x = x \]

### Step 4: Solve the equation
Now, we can solve the equation for \( x \):
1. Rearranging the equation gives:
\[ 52 = x + x \]
\[ 52 = 2x \]
2. Dividing both sides by 2:
\[ x = \frac{52}{2} \]
\[ x = 26 \]

### Step 5: Find the son's age 8 years ago
Now that we have the son's current age, which is 26 years, we can calculate his age 8 years ago:
\[ \text{Son's age 8 years ago} = 26 - 8 = 18 \]

### Conclusion
The son's age 8 years back was **18 years**.

---