Reenu father is thrice as old as reenu. After `12` years he will be just twice his daughter Find their present ages.

Options

A. `30` years and `18` years
B. `36` years and `12` years
C. `36` years and `10` years
D. `"none of these"`

Answer

To solve the problem step by step, let's denote Renu's current age as \( x \).

### Step 1: Define the Variables
Let Renu's age be \( x \).
Then, Renu's father's age will be \( 3x \) (since he is thrice as old as Renu).

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

### Step 2: Set Up the Equation for Future Ages
After 12 years, Renu's age will be \( x + 12 \) and her father's age will be \( 3x + 12 \).
According to the problem, after 12 years, Renu's father will be twice as old as Renu. Therefore, we can set up the equation:
\[ 3x + 12 = 2(x + 12) \]

**Hint:** Write down the expressions for their ages after 12 years and relate them according to the problem's conditions.

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

**Hint:** Remember to distribute the multiplication across the terms in the parentheses.

### Step 4: Rearrange the Equation
Next, we will move all terms involving \( x \) to one side and constant terms to the other side:
\[ 3x - 2x = 24 - 12 \]
This simplifies to:
\[ x = 12 \]

**Hint:** Combine like terms carefully to isolate the variable.

### Step 5: Find Renu's Father's Age
Now that we have Renu's age, we can find her father's age:
\[ \text{Father's age} = 3x = 3 \times 12 = 36 \]

**Hint:** Use the value of \( x \) to calculate the father's age based on the relationship defined at the beginning.

### Conclusion
Renu's current age is \( 12 \) years, and her father's current age is \( 36 \) years.

**Final Answer:** Renu is 12 years old, and her father is 36 years old.