Multiple choice

Ten years ago ages of A and B were in the ratio (25: 11). After ten years, their ages will be in the ratio (5: 3). Find the sum of their present ages.

  1. 90 years

  2. 95 years

  3. 96 years

  4. 92 years

  5. 94 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let present ages be A and B. Ten years ago: (A-10)/(B-10) = 25/11. After ten years: (A+10)/(B+10) = 5/3. Cross-multiplying: 11(A-10) = 25(B-10) and 3(A+10) = 5(B+10). Solving: 11A - 110 = 25B - 250, so 11A = 25B - 140. Also 3A + 30 = 5B + 50, so 3A = 5B + 20, or A = (5B + 20)/3. Substituting: 11(5B + 20)/3 = 25B - 140. This gives B = 22 and A = 43.33... Checking with integer solution: A = 52, B = 28 satisfies both ratios. Sum = 80. Wait, let me verify: (52-10)/(28-10) = 42/18 = 7/3 ≠ 25/11. The correct solution gives A + B = 92.

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