Past ratio with current difference: Two years ago A was twice as old as B. If their current age difference is 2 years, what is A's present age?

Introduction / Context:One condition at a past time and one present-day difference allow a quick linear solution.

Given Data / Assumptions:

• Let present ages be A and B with A − B = 2.
• Two years ago: A − 2 = 2(B − 2).

Concept / Approach:Express A in terms of B from the past condition, then use the present difference to solve B and A.

Step-by-Step Solution:1) From A − 2 = 2B − 4 ⇒ A = 2B − 2.2) Plug into A − B = 2 ⇒ (2B − 2) − B = 2 ⇒ B − 2 = 2 ⇒ B = 4.3) A = 2B − 2 = 6.

Verification / Alternative check:Two years ago: A=4, B=2 ⇒ A was twice B; difference now is 2. Checks out.

Why Other Options Are Wrong:They fail either the past doubling or the present difference.

Common Pitfalls:Subtracting 2 from only one age when shifting to “two years ago.”

Final Answer:6