Multiple choice

Ten years hence, the ratio of the ages of a father and his son will be 5 : 3, while 10 years ago, it was 3 : 1. The ratio of the present ages of the son and the father is

  1. 1 : 2

  2. 1 : 3

  3. 2 : 3

  4. 2 : 5

  5. 2 : 1
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AI explanation

Let the father's and son's present ages be F and S. Ten years hence the ratio is 5:3, so 3(F + 10) = 5(S + 10) or 3F - 5S = 20. Ten years ago the ratio was 3:1, so F - 10 = 3(S - 10) or F = 3S - 20. Substituting this into the first equation gives 3(3S - 20) - 5S = 20, which solves to 4S = 80 and S = 20. With F = 3(20) - 20 = 40, the ratio of the present ages of the son and the father is 20:40, or 1:2.

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