Multiple choice

X’s age 3 years ago was three times the present age of Y. at present, Z’s age is twice the age of Y. also Z is 12 years younger than X. what is the present age of Z?

  1. 18

  2. 12

  3. 15

  4. 24

  5. None of these
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A Correct answer
Explanation

X - 3 = 3Y. Z = 2Y. Z = X - 12. Substitute X = Z + 12 into the first equation: (Z + 12) - 3 = 3Y, so Z + 9 = 3Y. Since Y = Z/2, Z + 9 = 3(Z/2). 2Z + 18 = 3Z, so Z = 18.

AI explanation

Let Y's present age be y, making Z's present age 2y, and X's present age 3y plus 3. Since Z is 12 years younger than X, the equation is 2y equals 3y plus 3 minus 12. Solving 2y equals 3y minus 9 gives y equals 9, so Z's present age is 2 times 9, which is 18 years.

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