Multiple choice

The age of father is equal to the square of the age of his son. The sum of the age of the father and five times the age of the son is $66$ years. Find their ages.

  1. Son's age =$7$ years, Father's age= $49$ years.
  2. Son's age = $6$ years, Father's age= $36$ years.
  3. Son's age = $5$ years, Father's age= $25$ years.
  4. Son's age = $4$ years, Father's age= $16$ years.
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B Correct answer
Explanation

Let son's age be x. Father's age = x^2. Equation: x^2 + 5x = 66. x^2 + 5x - 66 = 0. (x + 11)(x - 6) = 0. x = 6. Father's age = 6^2 = 36.

AI explanation

Let the son's age be S and the father's age be F. We are given F = S^2 and F + 5S = 66. Substituting the first equation into the second gives S^2 + 5S minus 66 = 0. Factoring this quadratic equation gives (S + 11)(S minus 6) = 0, so S = 6. The father's age is 6^2 = 36. The son is 6 years old and the father is 36 years old.

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