Multiple choice

Six years hence, a man's age will be three times the age of his son and three years ago he was nine times as old as his son. The present age of the man is

  1. $28$ years
  2. $30$ years
  3. $32$ years
  4. $34$ years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M and S be the present ages. (M+6) = 3(S+6) => M = 3S + 12. (M-3) = 9(S-3) => M = 9S - 24. Setting them equal: 3S + 12 = 9S - 24 => 6S = 36 => S = 6. Then M = 3(6) + 12 = 30.

AI explanation

Let the present age of the son be x years and the man be y years. From the first condition, y + 6 = 3 times (x + 6), which simplifies to y = 3x + 12. From the second condition, y - 3 = 9 times (x - 3), which simplifies to y = 9x - 24. Equating the two expressions gives 3x + 12 = 9x - 24, meaning 6x = 36 and x = 6. Substituting x into the first equation gives y = 30, so the present age of the man is 30 years.

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