Multiple choice

Four years ago father's age was 6 times that of his son. Twelve years from now. father's age will be twice that of the son. What is the ratio of father and son's present ages ?

  1. $6 : 1$
  2. $7 : 1$
  3. $8 : 2$
  4. $7 : 2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let F, S be present ages. (F-4) = 6(S-4) => F-4 = 6S-24 => F = 6S-20. (F+12) = 2(S+12) => F+12 = 2S+24 => F = 2S+12. 6S-20 = 2S+12 => 4S = 32 => S = 8. F = 2(8)+12 = 28. Ratio F:S = 28:8 = 7:2.

AI explanation

Let the son's age four years ago be x, so the father's age then was 6x. Twelve years from now the son's age is x plus 16 and the father's age is 6x plus 16. Given 6x plus 16 equals 2 times x plus 16, solving gives 4x equals 16 and x equals 4. Their present ages are x plus 4 which is 8 and 6x plus 4 which is 28, giving the ratio 28 to 8 or 7:2.

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