Multiple choice

Five years later, A's age will be 3 times B. Five years ago, A's age was 8 times that of B. Find their present ages.

  1. Present age of A = 45 years Present age of B = 12 years

  2. Present age of A = 50 years Present age of B = 13 years

  3. Present age of A = 37 years Present age of B = 9 years

  4. Present age of A = 27 years Present age of B = 7 years

  5. Present age of A = 60 years Present age of B = 20 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A and B be present ages. (A+5) = 3(B+5) and (A-5) = 8(B-5). Solving: A+5 = 3B+15 => A-3B=10. A-5 = 8B-40 => A-8B=-35. Subtracting: 5B = 45 => B=9. A = 37.

AI explanation

Let A's present age be x and B's present age be y. Five years later, x + 5 = 3(y + 5), which simplifies to x = 3y + 10. Five years ago, x - 5 = 8(y - 5), which simplifies to x = 8y - 35. Setting the equations equal gives 3y + 10 = 8y - 35, so 5y = 45 and y = 9. Substituting y gives x = 3(9) + 10 = 37, meaning the present age of A is 37 years and the present age of B is 9 years.

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