Today is Varun's birthday. One year from today, he will be twice as old as he was 12 years ago. How old is Varun today in years?

Difficulty: Easy

Correct Answer: 25 years

Explanation:


Introduction / Context:
This is a straight numerical age puzzle that connects Varun's age one year from now with his age 12 years ago using a simple multiplicative relation. It is a classic example of forming and solving a single linear equation in one variable based on time shift statements.


Given Data / Assumptions:

  • Let Varun's present age be V years.
  • One year from today, his age will be V + 1.
  • Twelve years ago, his age was V - 12.
  • We are told that V + 1 is twice (V - 12).


Concept / Approach:
Translate the verbal statement into an algebraic equation, namely V + 1 = 2 * (V - 12). Then solve this equation for V. This gives Varun's present age directly. It is important to keep the time references consistent when forming the equation.


Step-by-Step Solution:
Let Varun's present age be V years. One year from today his age will be V + 1. Twelve years ago his age was V - 12. According to the problem, V + 1 = 2 * (V - 12). Expand the right side: V + 1 = 2V - 24. Rearrange terms: bring V to the right and -24 to the left. So 1 + 24 = 2V - V which gives 25 = V. Therefore Varun's present age V is 25 years.


Verification / Alternative check:
Check the condition: One year from now, Varun will be 26 years old. Twelve years ago, he was 25 - 12 = 13 years old. Twice that past age is 2 * 13 = 26, which matches his age one year from now. Hence the given relation holds exactly, confirming that 25 years is correct.


Why Other Options Are Wrong:
If Varun were 24 now, then one year from now he would be 25, but his age 12 years ago would be 12, and 2 * 12 = 24, not 25. Similar checks for 23 or 22 quickly show contradictions with the required condition. The option 26 fails as well, since the numbers no longer satisfy the equation V + 1 = 2 * (V - 12). Only 25 works perfectly.


Common Pitfalls:
A common error is to misread "one year from today" as "one year ago" or to incorrectly handle the difference between 12 years ago and 1 year ahead. Some learners also make algebraic mistakes when moving terms across the equality. Writing the equation slowly and checking it with the final value helps avoid these issues.


Final Answer:
So, Varun is 25 years old today.

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