Multiple choice

The sum of the ages of a father and his son is $48$ years. Six years ago, the father's age was five times the age of his son. Find their present ages.

  1. Present age of Father is $30$ years and

    Present age of son is  $10$  years
  2. Present age of Father is  $48$  years and

    Present age of son is  $16$  years
  3. Present age of Father is  $45$  years and

    Present age of son is $15$  years
  4. Present age of Father is $36$  years and

    Present age of son is  $12$  years
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D Correct answer
Explanation

Let F and S be present ages. F + S = 48. Six years ago: (F-6) = 5(S-6). F-6 = 5S-30 => F = 5S-24. Substitute: 5S-24 + S = 48 => 6S = 72 => S = 12. F = 36.

AI explanation

Let the son's present age be x years, making the father's age 48 minus x. Six years ago their ages were x minus 6 and 42 minus x, so the equation is 42 minus x equals 5 times x minus 6, which simplifies to 6x equals 72 and x equals 12. Therefore the father's present age is 48 minus 12 which is 36 years.

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