Multiple choice

At present, the sum of the ages of father and his son is 100 years. Five years ago, the ratio of their ages was 2 : 1. What will be the respective ratio of their ages after 10 years from now?

  1. 5 : 3

  2. 13 : 16

  3. 17 : 7

  4. 18 : 3

  5. 20 : 7
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A Correct answer
Explanation

Let ages be F and S. F+S = 100. Five years ago, (F-5)/(S-5) = 2/1, so F-5 = 2S-10, F = 2S-5. Substitute: 2S-5+S = 100, 3S = 105, S = 35, F = 65. After 10 years, ages are 75 and 45. Ratio 75:45 = 5:3.

AI explanation

Let the present age of the father be f and the son be s. The sum of their present ages is 100, so f plus s equals 100. Five years ago, their ages were f minus 5 and s minus 5, giving the equation f minus 5 equals 2 times s minus 5. Substituting f equals 100 minus s into the second equation yields 100 minus s minus 5 equals 2s minus 10, which simplifies to 3s equals 105, so s equals 35 and f equals 65. In 10 years, the father will be 75 and the son will be 45, making their ratio 75 to 45 or 5 to 3.

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