Multiple choice

Five years ago, A's age was four times the age of B. Five years hence, A's age will be twice the age of B. Find their present ages.

  1. Present age of $A = 29$ years and that of $B = 11$ years
  2. Present age of $A = 25$ years and that of $B = 10$ years
  3. Present age of $A = 65$ years and that of $B = 20$ years
  4. Present age of $A = 40$ years and that of $B = 10$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A and B be current ages. (A-5) = 4(B-5) => A - 4B = -15. (A+5) = 2(B+5) => A - 2B = 5. Subtracting equations: 2B = 20, so B = 10. Then A = 25.

AI explanation

Let the present age of A be x and the present age of B be y. Five years ago, x minus 5 equaled 4 times (y minus 5), simplifying to x equals 4y minus 15. Five years hence, x plus 5 will equal 2 times (y plus 5), simplifying to x equals 2y plus 5. Equating the two expressions gives 4y minus 15 equals 2y plus 5, meaning 2y equals 20 and y equals 10. Substituting 10 for y gives A's present age as 25 years.

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