Find today's age from a forward–backward relation: Today is Vishal's birthday. One year from today he will be twice as old as he was 12 years ago. How old is Vishal today?

Introduction / Context:Statements tying a future age to a past age convert neatly into linear equations. The key is to represent today's age with x, then express the future and past in terms of x ± k.

Given Data / Assumptions:

• Let current age be x.
• One year from now: x + 1.
• Twelve years ago: x − 12.
• Condition: x + 1 = 2(x − 12).

Concept / Approach:Translate the English sentence literally into an equation, then solve for x.

Step-by-Step Solution:1) x + 1 = 2x − 24.2) Bring terms together: −x = −25 ⇒ x = 25.3) Hence, Vishal is 25 years old today.

Verification / Alternative check:Check: One year from now, 26; twelve years ago, 13; 26 is twice 13. The condition holds exactly.

Why Other Options Are Wrong:They fail the equality x + 1 = 2(x − 12) when substituted.

Common Pitfalls:Misplacing the offsets (using 12 instead of 1 or vice versa), or forgetting that “one year from today” is x + 1, not x.

Final Answer:25 years