Multiple choice

Six years ago a man was three times as old as his son. In $6$ years time, he will be twice as old as his son. Find their present ages

  1. $30, 15$
  2. $40, 20$
  3. $42, 18$
  4. $41, 19$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M and S be current ages. (M-6) = 3(S-6) => M-3S = -12. (M+6) = 2(S+6) => M-2S = 6. Subtracting the first from the second: S = 18. Then M = 42.

AI explanation

Let the present age of the son be x years. Six years ago, the man's age was 3 times the son's age, meaning the man's present age is 3 times x minus 18 plus 6, which equals 3x minus 12. In 6 years, the man will be twice as old as his son, giving the equation 3x minus 12 plus 6 equals 2 times x plus 6. Solving this equation yields x equals 18, meaning the son is 18 years old. The man's present age is 3 times 18 minus 12, which equals 42 years.

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