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      Question

      Six years ago, A was four times as old as B. Six years

      from now, A will be twice as old as B. Find their present ages.
      A A = 50 years; B = 12 years. Correct Answer Incorrect Answer
      B A = 30 years; B = 12 years. Correct Answer Incorrect Answer
      C A = 30 years; B = 22 years. Correct Answer Incorrect Answer
      D A = 20 years; B = 12 years. Correct Answer Incorrect Answer

      Solution

      Let present ages be A years and B years. Six years ago: A − 6 = 4(B − 6) ...(1) Six years hence: A + 6 = 2(B + 6) ...(2) Expand (1): A − 6 = 4B − 24 A − 4B = −18 ...(i) Expand (2): A + 6 = 2B + 12 A − 2B = 6 ...(ii) Subtract (i) from (ii): (A − 2B) − (A − 4B) = 6 − (−18) −2B + 4B = 24 2B = 24 ⇒ B = 12 From (ii): A − 2 × 12 = 6 A − 24 = 6 ⇒ A = 30 Answer: Present ages: A = 30 years; B = 12 years.

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