12 years ago, Lila's age was equal to 1/9th her grandfather's age. After 8 years from now, her grandfather's age would be thrice her age. Which of the following gives the ratio of the present ages of Lila and her grandfather?

Let Lila's age 12 years ago be x, making her grandfather's age 9x at that time. Eight years from now, which is 20 years after that initial point, their ages will be x + 20 and 9x + 20; setting up the equation gives 9x + 20 = 3(x + 20). Solving this yields 6x = 40, so x = 20/3. Their present ages are 20/3 + 12 = 56/3 and 9(20/3) + 12 = 72, making their ratio (56/3) : 72, which simplifies to 7 : 27.

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