Multiple choice

The sum of the ages of a father and his son is 100 years now. 5 years ago their ages were in the ratio (2 : 1). The ratio of the ages of father and son after 10 years will be

  1. $5 : 3$
  2. $4 : 3$
  3. $10 : 7$
  4. $3 : 5$
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A Correct answer
Explanation

Let current ages be f and s. f + s = 100. Five years ago: (f-5)/(s-5) = 2/1, so f-5 = 2s-10, giving f = 2s-5. Substituting: 2s-5 + s = 100, so 3s = 105, s = 35, f = 65. After 10 years: (75)/(45) = 5/3.

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