Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. The average of the ages of a man and his son is 35 years. After 10 years, the ratio of their ages will be 2:1. What is the son's present age in years?
A. 15
B. 16
C. 20
D. 25
E. none of these
Explanation: (C) Let F be the man's age and S be the son's age. (i) \(\frac{F + S}{2} = 35 \implies F + S = 70\). (ii) After 10 years, the ratio of their ages will be 2:1: \(\frac{F + 10}{S + 10} = 2\). \(F + 10 = 2(S + 10) \implies F + 10 = 2S + 20 \implies F = 2S + 10\). Substitute F from (ii) into (i): \((2S + 10) + S = 70 \implies 3S = 60 \implies S = 20\). The son's present age is 20 years.
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