Vipin is 42 years old and his son is 12 years old. After how many years will Vipin's age be twice that of his son?

Answer

To solve the problem, we need to determine after how many years Vipin's age will be twice that of his son's age.

Let's break it down step by step:

### Step 1: Define the current ages
- Vipin's current age = 42 years
- Son's current age = 12 years

### Step 2: Define the variable for years
Let \( x \) be the number of years after which Vipin's age will be twice that of his son's age.

### Step 3: Write the expressions for their ages after \( x \) years
- Vipin's age after \( x \) years = \( 42 + x \)
- Son's age after \( x \) years = \( 12 + x \)

### Step 4: Set up the equation
According to the problem, after \( x \) years, Vipin's age will be twice his son's age. Therefore, we can set up the equation:
\[ 42 + x = 2(12 + x) \]

### Step 5: Expand and simplify the equation
Expanding the right side:
\[ 42 + x = 24 + 2x \]

Now, rearranging the equation to isolate \( x \):
\[ 42 - 24 = 2x - x \]
\[ 18 = x \]

### Step 6: Conclusion
Thus, \( x = 18 \). This means after 18 years, Vipin's age will be twice that of his son.

### Final Answer
After 18 years, Vipin's age will be twice that of his son.

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