The age of the father 5 years ago was 5 times the age of his son. At present the father's age is 3 times that of his son. What is the present age of the father?

Options

A. 33 years
B. 30 years
C. 45 years
D. None of these

Answer

To solve the problem, we will set up equations based on the information provided in the question.

### Step 1: Define the variables
Let:
- \( x \) = present age of the father
- \( y \) = present age of the son

### Step 2: Set up the equations
From the problem, we have two key pieces of information:
1. The age of the father 5 years ago was 5 times the age of his son at that time.
2. The father's current age is 3 times the son's current age.

From the first piece of information, we can write the equation:
\[ x - 5 = 5(y - 5) \]
This simplifies to:
\[ x - 5 = 5y - 25 \]
Rearranging gives us:
\[ x - 5y = -20 \quad \text{(Equation 1)} \]

From the second piece of information, we can write the equation:
\[ x = 3y \quad \text{(Equation 2)} \]

### Step 3: Substitute Equation 2 into Equation 1
Now, we can substitute \( x \) from Equation 2 into Equation 1:
\[ 3y - 5y = -20 \]
This simplifies to:
\[ -2y = -20 \]

### Step 4: Solve for \( y \)
Dividing both sides by -2 gives:
\[ y = 10 \]
So, the present age of the son is 10 years.

### Step 5: Find the present age of the father
Now, we can use Equation 2 to find the father's age:
\[ x = 3y = 3 \times 10 = 30 \]
Thus, the present age of the father is 30 years.

### Final Answer
The present age of the father is **30 years**.

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