Multiple choice

Five years ago, the ratio of the ages of A and B was 10 : 11. After 7 years from now, the ratio of the ages of A and B will be 22 : 23. Find the present ages of A and B.

  1. 14 years and 15 years

  2. 19 years and 20 years

  3. 15 years and 16 years

  4. 17 years and 16 years

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let ages 5 years ago be 10x and 11x. Present ages are 10x+5 and 11x+5. After 7 years, ages are 10x+12 and 11x+12. Ratio (10x+12)/(11x+12) = 22/23. Solving gives 230x + 276 = 242x + 264, so 12x = 12, x = 1. Present ages are 15 and 16.

AI explanation

Let their present ages be A and B. Five years ago, (A - 5) / (B - 5) = 10/11, which gives 11A - 10B = 5. Seven years from now, (A + 7) / (B + 7) = 22/23, which gives 23A - 22B = -8. Solving this system of linear equations yields A = 15 and B = 16. The present ages of A and B are 15 years and 16 years respectively.

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