Rahul father is thrice as old as Rahul after `12` years he will be just twice his son. Find the present of Rahul's father.

Options

A. `42` years
B. `24` years
C. `36` years
D. `63` years

Answer

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

### Step 1: Define the Variables
Let Rahul's present age be \( x \).

### Step 2: Express Father's Age
According to the problem, Rahul's father is thrice as old as Rahul. Therefore, we can express the father's age as:
\[ \text{Father's age} = 3x \]

### Step 3: Set Up the Future Age Equation
After 12 years, Rahul's age will be:
\[ \text{Rahul's age after 12 years} = x + 12 \]
And the father's age will be:
\[ \text{Father's age after 12 years} = 3x + 12 \]

According to the problem, after 12 years, the father's age will be twice Rahul's age. We can set up the equation:
\[ 3x + 12 = 2(x + 12) \]

### Step 4: Expand the Equation
Now, we will expand the right side of the equation:
\[ 3x + 12 = 2x + 24 \]

### Step 5: Rearrange the Equation
Next, we will rearrange the equation to isolate \( x \):
1. Subtract \( 2x \) from both sides:
\[ 3x - 2x + 12 = 24 \]
\[ x + 12 = 24 \]

2. Now, subtract 12 from both sides:
\[ x = 24 - 12 \]
\[ x = 12 \]

### Step 6: Find Father's Present Age
Now that we have Rahul's age, we can find the father's age:
\[ \text{Father's age} = 3x = 3 \times 12 = 36 \]

### Conclusion
Thus, the present age of Rahul is \( 12 \) years and the present age of his father is \( 36 \) years.

### Final Answer
- Rahul's present age: 12 years
- Father's present age: 36 years

---