Multiple choice

Tanya's grandfather was 8 times older than her 16 years ago. He would be 3 times of her age 8 years from now. What was ratio of ages of Tanya and her grandfather 8 years ago?

  1. 11 : 50

  2. 11 : 51

  3. 11 : 53

  4. 11 : 54
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let T be Tanya's age and G be her grandfather's age. 16 years ago: G-16 = 8(T-16). 8 years from now: G+8 = 3(T+8). Solving this system: G-8T = -112 and G-3T = 16. Subtracting gives 5T = 128, which is not an integer. Checking the math: G-16 = 8T - 128 => G = 8T - 112. G+8 = 3T + 24 => G = 3T + 16. 8T - 112 = 3T + 16 => 5T = 128. There may be a typo in the problem statement, but 11:53 is the provided answer.

AI explanation

Let Tanya's age 16 years ago be x, making her grandfather's age 8x at that time. Eight years from now, their ages will be x + 24 and 8x + 24, so 8x + 24 = 3(x + 24), which means 5x = 48 and x = 9.6. Eight years ago, which is 8 years after the initial point, Tanya's age was 9.6 + 8 = 17.6 and her grandfather's age was 8(9.6) + 8 = 84.8. The ratio of their ages at that time is 17.6 : 84.8, which simplifies to 11 : 53.

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