Multiple choice

Father's age is three times the sum of ages of his two children. After $5$ years his age will be twice the sum of ages of two children. Find the age of father.

  1. Father's age $= 75$ years
  2. Father's age $= 45$ years
  3. Father's age $= 66$ years
  4. Father's age $= 88$ years
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B Correct answer
Explanation

Let F = father's age, S = sum of children's ages. F = 3S. (F+5) = 2(S+10). Substitute F: 3S + 5 = 2S + 20, so S = 15. F = 3 * 15 = 45.

AI explanation

Let the sum of the present ages of the two children be x years, which makes the father's present age 3x years. After 5 years, the sum of the children's ages will be x + 10, and the father's age will be 3x + 5. The problem states that 3x + 5 equals 2 times x + 10, so 3x + 5 = 2x + 20. Solving this linear equation gives x = 15, and therefore the father's age is 3 times 15, which is 45 years.

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