Multiple choice

Seven years ago, the ratio of the ages of A and B was (4 \colon 5). Eight years hence, the ratio of the ages of A and B will be (9 \colon 10). What is the sum of their present ages in years?

  1. 32 years

  2. 41 years

  3. 56 years

  4. 82 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let present ages be A and B. Seven years ago: (A-7)/(B-7) = 4/5, so 5A - 35 = 4B - 28, giving 5A - 4B = 7. In eight years: (A+8)/(B+8) = 9/10, so 10A + 80 = 9B + 72, giving 10A - 9B = -8. Solving: A = 19, B = 22, so sum = 41 years.

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