Parent–child ages with a future double condition: My father is 21 years older than me. In 12 years, his age will be twice mine. How old am I now?

Introduction / Context:Future multiple conditions with a known present difference translate into an equation in one variable. Represent your present age as x; father's present age is x + 21. Use the future-time doubling relation to solve for x.

Given Data / Assumptions:

• Father now = x + 21.
• In 12 years: father = 2 × (my age then).

Concept / Approach:Set up (x + 21 + 12) = 2(x + 12) and solve for x directly.

Step-by-Step Solution:1) x + 33 = 2x + 24.2) 33 − 24 = 2x − x ⇒ 9 = x.3) Therefore, my present age is 9 years.

Verification / Alternative check:In 12 years: me = 21, father = 30; indeed, 30 is twice 15? Wait—recompute correctly: me then = 9 + 12 = 21; father then = (9 + 21) + 12 = 42; 42 = 2 × 21 (true). Condition satisfied.

Why Other Options Are Wrong:

• 8/10/11/12 years do not satisfy the future double relation with a 21-year current difference.

Common Pitfalls:Adding 12 to the difference (which must remain 21) or misapplying the doubling to present ages instead of future ages leads to errors.

Final Answer:9 years