Karthik is currently 32 years old and his son is 7 years old. After how many years from now will Karthik be exactly twice as old as his son?

Introduction / Context:
This is a classic problems on ages question from quantitative aptitude. It checks whether you can translate a simple English statement about present and future ages into an equation in one variable and then find the time after which one person becomes a multiple of another person age. Such questions are very common in bank exams, campus placements, and other competitive tests.

Given Data / Assumptions:

• Karthik present age is 32 years.
• His son present age is 7 years.
• We need the number of years from now after which Karthik age will be exactly twice the age of his son.
• Both ages increase at the same rate, that is by the same number of years as time passes.

Concept / Approach:
The key idea in problems on ages is to define a variable for the unknown quantity, usually the present age or the required time. Then we express future or past ages in terms of this variable and form an equation from the given condition. Here the condition is that after some years, the father age becomes twice the son age. That single relationship leads to one linear equation in one variable, which is easy to solve using basic algebra. Finally, we verify by substituting the result back into the condition.

Step-by-Step Solution:
Step 1: Let the required number of years from now be t. Step 2: After t years, Karthik age will be 32 + t. Step 3: After the same t years, the son age will be 7 + t. Step 4: The condition says that at that time, father age is twice the son age, so set up the equation 32 + t = 2 × (7 + t). Step 5: Solve this linear equation to get the value of t, which comes out to 18. Step 6: Therefore, after 18 years, Karthik age will be twice his son age.

Verification / Alternative check:
After 18 years, Karthik age will be 32 + 18 = 50 years. His son age will be 7 + 18 = 25 years. Now check the relationship: 50 is exactly 2 times 25, so the condition is perfectly satisfied. This confirms that the equation was set correctly and that no logical mistake was made in interpreting the wording of the question.

Why Other Options Are Wrong:
Option 25: After 25 years, ages would be 57 and 32, and 57 is not twice 32, so this is incorrect.
Option 7: After 7 years, ages would be 39 and 14, and 39 is not twice 14, so this is incorrect.
Option 15: After 15 years, ages would be 47 and 22, and 47 is not twice 22, so this is also incorrect.
Option 20: After 20 years, ages would be 52 and 27, and 52 is not twice 27, so this fails the condition as well.

Common Pitfalls:
A common mistake is to try to make the present age of Karthik twice the present age of his son, which is not what the question says. Another frequent error is to write the wrong equation, for example 32 + t = 2 × 7 + t, which misses the fact that the son age also increases by t. Always ensure that all people ages move forward or backward by the same number of years when you deal with future or past situations.

Final Answer:
The required number of years after which Karthik will be twice as old as his son is 18 years.