Multiple choice

A's age was 8 times B's age 16 years ago. A would be 4 times of B's age 8 years from now. What was the ratio of ages of A and B 8 years ago?

  1. 76 : 13

  2. 53 : 11

  3. 53 : 12

  4. 11 : 51

  5. None of these
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A Correct answer
Explanation

Let A and B be current ages. (A-16) = 8(B-16) and (A+8) = 4(B+8). Solving the system: A-8B = -112 and A-4B = 24. Subtracting gives 4B = 136, so B = 34 and A = 160. Eight years ago, ages were 152 and 26. The ratio is 152:26 = 76:13.

AI explanation

Let the present ages of A and B be A and B; 16 years ago the equation was A - 16 = 8(B - 16), simplifying to A - 8B = -112. For 8 years from now, A + 8 = 4(B + 8), which simplifies to A - 4B = 24. Subtracting the first equation from the second gives 4B = 136, so B = 34 and A = 160. Eight years ago, their ages were 152 and 26, making the requested ratio 76 : 13.

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