Multiple choice

The age of a person k years ago was half of what his age would be k years from now. The age of the same person p years from now would be thrice of what his age was p years ago. What is the value of the ratio k:p?

  1. $3:2$
  2. $2:3$
  3. $1:4$
  4. $4:1$
  5. $5:1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let current age be x. (x-k) = 1/2 * (x+k) => 2x - 2k = x + k => x = 3k. Also (x+p) = 3 * (x-p) => x + p = 3x - 3p => 4p = 2x => x = 2p. So 3k = 2p, which means k/p = 2/3.

AI explanation

Let the present age be x. Then x minus k equals half of x plus k, so 2x minus 2k equals x plus k, giving x equals 3k. Also x plus p equals 3 times x minus p, so x plus p equals 3x minus 3p, which simplifies to 2x equals 4p or x equals 2p. Equating the two expressions gives 3k equals 2p, therefore the ratio k:p is 2:3.

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