Multiple choice

The present age of a father is equal to the sum of the ages of his $5$ children. $12$ years hence, the sum of the ages of his children will be twice the age of their father. Find the present age of the father.

  1. $32$ years
  2. $34$ years
  3. $36$ years
  4. $38$ years
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C Correct answer
Explanation

Let F be the father's age and S be the sum of the children's ages. We have F = S. In 12 years, the sum of the children's ages will be S + 5(12) = S + 60, and the father's age will be F + 12. Given S + 60 = 2(F + 12), substitute S = F to get F + 60 = 2F + 24, which simplifies to F = 36.

AI explanation

Let the sum of the present ages of the 5 children be x, making the father's present age x as well. After 12 years, the sum of the children's ages will be x + 60, and the father's age will be x + 12. The problem states that x + 60 = 2(x + 12), which simplifies to x + 60 = 2x + 24, yielding x = 36. The present age of the father is 36 years.

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