Multiple choice

Five years hence, father's age will be three times the age of his son. Five years ago, father was seven times as old as his son. Find their present ages

  1. Father's age $= 80$ years, Son's age $= 25$ years
  2. Father's age $= 60$ years, Son's age $= 30$ years
  3. Father's age $= 75$ years, Son's age $= 42$ years
  4. Father's age $= 40$ years, Son's age $= 10$ years
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D Correct answer
Explanation

Let F and S be present ages. (F+5) = 3(S+5) => F - 3S = 10. (F-5) = 7(S-5) => F - 7S = -30. Subtracting equations: 4S = 40, so S = 10. Then F = 40.

AI explanation

Let the present age of the son be x years and the father be y years. From the first condition, y + 5 = 3 times (x + 5), which simplifies to y = 3x + 10. From the second condition, y - 5 = 7 times (x - 5), which simplifies to y = 7x - 30. Equating the two expressions gives 3x + 10 = 7x - 30, so 4x = 40 and x = 10. Substituting x into the first equation gives y = 40, meaning the father is 40 years old and the son is 10 years old.

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