Multiple choice

4 year's ago, the ratio of ½ of A's age at that time and four times of B's age at the time was 5:12. Eight year's hence, ½ of A's age at that time will be less than B's age at that time by 2 years. What is B's present age?

  1. 20 years

  2. 14 years

  3. 12 years

  4. 10 years

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A and B be present ages. 4 years ago: (A-4)/2 / 4(B-4) = 5/12 => (A-4) / 8(B-4) = 5/12 => 12A - 48 = 40B - 160 => 12A - 40B = -112 => 3A - 10B = -28. 8 years hence: (A+8)/2 = (B+8) - 2 => A+8 = 2B + 12 => A - 2B = 4 => A = 2B + 4. Substitute: 3(2B+4) - 10B = -28 => 6B + 12 - 10B = -28 => -4B = -40 => B = 10.

AI explanation

Four years ago, half of A's age was 5x and four times B's age was 12x, meaning A's age four years ago was 10x and B's was 3x. Their present ages are 10x plus 4 and 3x plus 4. Eight years hence, half of A's age is less than B's age by 2, giving the equation half of 10x plus 12 equals 3x plus 12 minus 2. Solving 5x plus 6 equals 3x plus 10 yields x equals 2, so B's present age is 3 times 2 plus 4, which is 10 years.

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