Birthday algebra – Today is Ketan’s birthday. One year from today he will be twice as old as he was 10 years ago. How old is Ketan today?

Introduction / Context:This single-variable age equation tests translating “one year from today” and “10 years ago” into algebra. Correctly placing the time shifts on the same unknown is the key step.

Given Data / Assumptions:

• Let Ketan’s present age be x years.
• One year from now: x + 1.
• Ten years ago: x − 10.
• Condition: x + 1 is twice (x − 10).

Concept / Approach:Write the equation (x + 1) = 2(x − 10) and solve for x. Ensure both references (future and past) are based on the same present variable.

Step-by-Step Solution:x + 1 = 2x − 20.Bring terms together: 1 + 20 = 2x − x ⇒ 21 = x.Therefore, Ketan is 21 years old today.

Verification / Alternative check:If x = 21, then one year later = 22. Ten years ago = 11. Twice 11 = 22, which matches.

Why Other Options Are Wrong:Other numbers do not satisfy x + 1 = 2(x − 10) when substituted.

Common Pitfalls:Applying the “twice” to the future age instead of the past age, or mixing up the 10-year offset signs.

Final Answer:21 years