Multiple choice

The present ages of three persons are in the ratio $4:7:9$. Eight years ago the sum of their ages was $56$. Find their present ages(in years).

  1. $16$ years, $28$ years, $36$ years
  2. $8$ years, $14$ years, $18$ years
  3. $12$ years, $21$ years, $29$ years

  4. None of the above
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A Correct answer
Explanation

Let ages be 4x, 7x, 9x. Eight years ago, ages were 4x-8, 7x-8, 9x-8. Sum = 20x - 24 = 56 => 20x = 80 => x = 4. Present ages: 16, 28, 36.

AI explanation

Let the present ages of the three persons be 4x, 7x, and 9x. Eight years ago their ages were 4x minus 8, 7x minus 8, and 9x minus 8, summing to 20x minus 24. Setting this equal to 56 gives 20x = 80, so x = 4. Multiplying the ratio values by 4 gives their present ages as 16, 28, and 36 years.

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