The age of a father is twice that of his son's at present age. After 5 years the sum of their ages will be 85. How old are they now?

Options

A. 40, 20
B. 46,23
C. 60,30
D. 50,25

Explanation

To solve the problem, we need to find the current ages of the father and son based on the information given. Let's break it down step by step.

### Step 1: Define Variables
Let the present age of the son be \( x \). Since the father's age is twice that of the son's, the present age of the father will be \( 2x \).

**Hint:** Start by defining the variables based on the relationships given in the problem.

### Step 2: Set Up the Equation for Future Ages
After 5 years, the son's age will be \( x + 5 \) and the father's age will be \( 2x + 5 \). According to the problem, the sum of their ages after 5 years will be 85.

So, we can write the equation:
\[ (x + 5) + (2x + 5) = 85 \]

**Hint:** Write an equation that represents the total of their ages after 5 years.

### Step 3: Simplify the Equation
Now, simplify the equation:
\[ x + 5 + 2x + 5 = 85 \]
Combine like terms:
\[ 3x + 10 = 85 \]

**Hint:** Combine the terms carefully to simplify the equation.

### Step 4: Solve for \( x \)
Next, isolate \( x \) by subtracting 10 from both sides:
\[ 3x = 85 - 10 \]
\[ 3x = 75 \]
Now, divide both sides by 3:
\[ x = \frac{75}{3} \]
\[ x = 25 \]

**Hint:** Perform operations to isolate the variable and solve for it.

### Step 5: Find the Ages
Now that we have \( x = 25 \), we can find the ages:
- The son's present age is \( x = 25 \).
- The father's present age is \( 2x = 2 \times 25 = 50 \).

**Hint:** Use the value of \( x \) to find both ages.

### Conclusion
The present age of the son is 25 years, and the present age of the father is 50 years.

**Final Answer:**
- Son's age: 25 years
- Father's age: 50 years