Multiple choice

The difference between the ages of a father and his son is 24 years. Three years ago, the ratio of ages of the father and the son was 8 : 5. What is the present age of the son?

  1. 53 years

  2. 46 years

  3. 43 years

  4. 63 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let F and S be current ages. F - S = 24. Three years ago: (F-3)/(S-3) = 8/5. 5F - 15 = 8S - 24. 5F - 8S = -9. Substitute F = S + 24: 5(S+24) - 8S = -9. 5S + 120 - 8S = -9. -3S = -129. S = 43.

AI explanation

Let the present ages of father and son be F and S. The difference is 24 years, so F - S = 24, which means F = S + 24. Three years ago, the ratio was 8 : 5, giving (S + 21) / (S - 3) = 8 / 5; cross-multiplying yields 5S + 105 = 8S - 24. Solving for S gives 3S = 129, so the present age of the son is 43 years.

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