Multiple choice

The ratio between the ages of a father and his son four years ago was 19 : 6. If the difference between the ages of the father and son is 26 years, what will be the ratio of their present ages?

  1. 21 : 8

  2. 23 : 8

  3. 23 : 10

  4. 27 : 14

  5. None of these
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A Correct answer
Explanation

Let father's age be F and son's be S. F - S = 26. Four years ago: (F-4)/(S-4) = 19/6. 6F - 24 = 19S - 76. 6F - 19S = -52. Substitute F = S + 26: 6(S+26) - 19S = -52. 6S + 156 - 19S = -52. -13S = -208. S = 16. F = 42. Present ratio = 42:16 = 21:8.

AI explanation

The difference between the ages of the father and son is a constant 26 years. Four years ago, their age ratio was 19 : 6, meaning the difference of 13 parts equaled 26 years, so each part equals 2 years. Four years ago, their ages were 19 times 2 equal to 38 years and 6 times 2 equal to 12 years. Adding 4 years to both gives their present ages as 42 and 16, making the ratio of their present ages 42 to 16, which simplifies to 21 : 8.

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