Multiple choice

If 6 years ago, the ratio of ages of A and B was 10 : 7 and 9 years hence, the ratio will be 13 : 10, then their respective present ages are

  1. 56 years and 41 years

  2. 50 years and 35 years

  3. 39 years and 30 years

  4. 56 years and 31 years

  5. None of these
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A Correct answer
Explanation

Let ages 6 years ago be 10x and 7x. Present ages are 10x+6 and 7x+6. Nine years hence, ages are 10x+15 and 7x+15. Ratio (10x+15)/(7x+15) = 13/10. 100x+150 = 91x+195, so 9x=45, x=5. Present ages: 10(5)+6=56 and 7(5)+6=41.

AI explanation

Let the present ages of A and B be x and y. The conditions give (x - 6) / (y - 6) = 10 / 7, which simplifies to 7x - 10y = -18; and (x + 9) / (y + 9) = 13 / 10, which simplifies to 10x - 13y = 27. Solving this system of linear equations yields x = 56 and y = 41. Their respective present ages are 56 years and 41 years.

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