A father's age is one more than 5 times of his son's age. After 3 years, the father's age would be 2 less than four times the son's age. Find the present age of the father.

Options

A. 30 years
B. 40 years
C. 31 years
D. 29 years

Explanation

To solve the problem step by step, we will define the variables and set up the equations based on the information provided.

### Step 1: Define the variables
Let the son's current age be \( x \) years.

### Step 2: Express the father's age in terms of the son's age
According to the problem, the father's age is one more than five times the son's age. Therefore, we can express the father's age as:
\[ \text{Father's age} = 5x + 1 \]

### Step 3: Set up the equation for their ages after 3 years
After 3 years, the father's age will be:
\[ (5x + 1) + 3 = 5x + 4 \]
After 3 years, the son's age will be:
\[ x + 3 \]
According to the problem, after 3 years, the father's age will be 2 less than four times the son's age. Therefore, we can write the equation:
\[ 5x + 4 = 4(x + 3) - 2 \]

### Step 4: Simplify the equation
Now, let's simplify the right side of the equation:
\[ 4(x + 3) - 2 = 4x + 12 - 2 = 4x + 10 \]
So, we have:
\[ 5x + 4 = 4x + 10 \]

### Step 5: Solve for \( x \)
Now, we will isolate \( x \):
\[ 5x - 4x = 10 - 4 \]
\[ x = 6 \]

### Step 6: Find the father's current age
Now that we have the son's age (\( x = 6 \)), we can find the father's age:
\[ \text{Father's age} = 5x + 1 = 5(6) + 1 = 30 + 1 = 31 \]

### Conclusion
The present age of the father is \( 31 \) years.

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