Rajan’s age is 3 times that of Ashok. After 12 years, Rajan’s age will be double the age of Ashok. Rajan’s present age is-

Options

A. 27 years
B. 32 years
C. 36 years
D. 40 years

Answer

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

### Step 1: Define the ages
- Rajan's age is given as 3 times Ashok's age. Therefore, we can express Rajan's age as:
\[ \text{Rajan's age} = 3X \]

### Step 2: Set up the equation for future ages
- After 12 years, Rajan's age will be:
\[ 3X + 12 \]
- After 12 years, Ashok's age will be:
\[ X + 12 \]

### Step 3: Create the equation based on the problem statement
- The problem states that after 12 years, Rajan's age will be double Ashok's age. Therefore, we can set up the equation:
\[ 3X + 12 = 2(X + 12) \]

### Step 4: Simplify the equation
- Expanding the right side of the equation gives us:
\[ 3X + 12 = 2X + 24 \]

### Step 5: Rearranging the equation
- Now, we can rearrange the equation to isolate \( X \):
\[ 3X - 2X = 24 - 12 \]
\[ X = 12 \]

### Step 6: Calculate Rajan's present age
- Now that we have Ashok's age, we can find Rajan's age:
\[ \text{Rajan's age} = 3X = 3 \times 12 = 36 \]

### Final Answer
- Rajan's present age is **36 years**.

---