Multiple choice

The present ages of three persons are in the proportion 4:7:9. Eight years ago, the sum of their ages was 56 years. The present age of the eldest person is ?

  1. 36 years

  2. 45 years

  3. 28 years

  4. 30 years

  5. None of these
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A Correct answer
Explanation

Let ages be 4x, 7x, 9x. 8 years ago: (4x-8) + (7x-8) + (9x-8) = 56. 20x - 24 = 56, 20x = 80, x = 4. Eldest person = 9x = 36.

AI explanation

Let the present ages of the three persons be 4x, 7x, and 9x. The sum of their present ages is 4x + 7x + 9x = 20x. Eight years ago, the sum of their ages was (4x - 8) + (7x - 8) + (9x - 8) = 20x - 24. We are given that this past sum equals 56, so 20x - 24 = 56. Solving for x gives 20x = 80, meaning x = 4. The eldest person's present age is the largest ratio multiplied by 4, which is 9 multiplied by 4, equaling 36 years.

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