Let the present age of the son be x years, so the father’s present age is 3x years. After 10 years, their ages will be x + 10 and 3x + 10 respectively. According to the given ratio, (3x + 10) : (x + 10) = 2 : 1, which leads to the equation 3x + 10 = 2(x + 10). Simplifying, 3x + 10 = 2x + 20 gives x = 10, so the son is presently 10 years old.
Option A:
Option A, 8 years, would make the father’s present age 24 and their ages after 10 years 18 and 34, giving a ratio of 34 : 18, which simplifies to 17 : 9, not 2 : 1. Thus, it fails the future ratio condition.
Option B:
Option B, 9 years, would give the father’s present age as 27 and future ages as 19 and 37, yielding 37 : 19, which is not 2 : 1.
Option C:
Option C satisfies both the present and future conditions: the father is 30 and son is 10 now, and after 10 years they will be 40 and 20, giving a ratio of 2 : 1. This consistency confirms 10 years as the correct present age of the son.
Option D:
Option D, 12 years, leads to a father’s present age of 36 and future ages of 22 and 46, giving the ratio 46 : 22 = 23 : 11, which again does not match the required 2 : 1.
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