Multiple choice

In $12$ years, a man will be three times as old as his son; the difference of their present ages is $30$ years. Find their present ages.

  1. $33$ years and $3$ years
  2. $50$ years and $10$ years
  3. $42$ years and $ 12 $ years
  4. $33$ years and $12$ years
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A Correct answer
Explanation

Let son's age be x, man's age be x+30. In 12 years: x+30+12 = 3(x+12). x+42 = 3x+36. 2x = 6, x = 3. Son is 3, man is 33.

AI explanation

Let the present age of the son be x years; since the difference of their present ages is 30 years, the man's present age is (x + 30) years. In 12 years, the son will be (x + 12) years old and the man will be (x + 42) years old. Setting up the equation based on the given condition gives x + 42 = 3 times (x + 12), which simplifies to x + 42 = 3x + 36. Solving this linear equation yields 2x = 6, so x = 3; therefore, the son is 3 years old and the man is 33 years old.

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