Twelve years ago, the ratio of the ages of Sarah and John was 4 : 5. If the present ratio of their ages is 7 : 8, then how much older is the older person compared to the younger person?

Let the present ages of Sarah and John be 7x and 8x years respectively. Twelve years ago, their ages were (7x - 12) and (8x - 12), giving the equation (7x - 12) / (8x - 12) = 4 / 5. Cross-multiplying yields 35x - 60 = 32x - 48, which simplifies to 3x = 12 and gives x = 4. The difference between their present ages is 8x - 7x = x, which equals 4 years.

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