Multiple choice

Four years ago a man was 6 times as old as his son.After 16 years he will be twice as old as his son. Whatis the present age of man and his son?

  1. 34,9

  2. 36,8

  3. 33,6

  4. 30,13

  5. 32,8
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A Correct answer
Explanation

Let M and S be current ages. (M-4) = 6(S-4) => M-6S = -20. (M+16) = 2(S+16) => M-2S = 16. Subtracting equations: 4S = 36, so S = 9. Then M = 34.

AI explanation

Let the son's present age be x years and the man's present age be y years. Four years ago, their ages were x - 4 and y - 4, giving the equation y - 4 = 6(x - 4), which simplifies to y = 6x - 20. After 16 years, their ages will be x + 16 and y + 16, so y + 16 = 2(x + 16), which simplifies to y = 2x + 16. Equating the two expressions for y gives 6x - 20 = 2x + 16, meaning 4x = 36 and x = 9. Substituting x back into the first equation gives y = 6(9) - 20 = 34, so the present ages are 34 and 9.

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