Multiple choice

10 years ago the age of the father was 5 times that of the son. 20 years hence the age of the father will be twice that of the son. The present age of the father (in years) is

  1. $40$
  2. $45$
  3. $60$
  4. $70$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let F and S be present ages. 10 years ago: F-10 = 5(S-10) => F = 5S - 40. 20 years hence: F+20 = 2(S+20) => F = 2S + 20. 5S - 40 = 2S + 20 => 3S = 60 => S = 20. F = 2(20) + 20 = 60.

AI explanation

Let the present age of the father be x years and the son be y years. Based on the conditions, x minus 10 equals 5 times y minus 10, which expands to x minus 5y equals minus 40. The second condition states x + 20 equals 2 times y + 20, which expands to x minus 2y equals 20. Subtracting the second equation from the first gives minus 3y equals minus 60, so y = 20. Substituting 20 for y gives x minus 40 equals 20, which means x equals 60, so the father is 60 years old.

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