A father is 30 years older than his son . In 12 years the man will be three times as old as his son. Find their present ages.

Options

A. 27 years 3 years
B. 30 years 3 years
C. 33 years ,3 years
D. 25 years 5 years

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define the Variables
Let the present age of the son be \( x \) years. Since the father is 30 years older than the son, the father's present age will be \( x + 30 \) years.

### Step 2: Set Up the Equation for Future Ages
In 12 years, the son’s age will be \( x + 12 \) years, and the father's age will be \( (x + 30) + 12 = x + 42 \) years.

### Step 3: Write the Equation Based on the Given Condition
According to the problem, in 12 years, the father will be three times as old as the son. Therefore, we can set up the equation:
\[ x + 42 = 3(x + 12) \]

### Step 4: Simplify the Equation
Now, let's simplify the equation:
\[ x + 42 = 3x + 36 \]

### Step 5: Rearrange the Equation
To isolate \( x \), we can rearrange the equation:
\[ x + 42 - 36 = 3x \]
\[ x + 6 = 3x \]

### Step 6: Solve for \( x \)
Now, subtract \( x \) from both sides:
\[ 6 = 3x - x \]
\[ 6 = 2x \]
Now, divide both sides by 2:
\[ x = 3 \]

### Step 7: Find the Present Ages
Now that we have \( x \), which is the son's age, we can find the father's age:
- Son's age = \( x = 3 \) years
- Father's age = \( x + 30 = 3 + 30 = 33 \) years

### Final Answer
The present ages are:
- Son: 3 years
- Father: 33 years

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