The ratio of the ages of the father and the son at present is 7 : After 4 years the ratio will become 4 : 1, what is the sum of the present ages of the father and the son ?

32 years
35 years
29 years
38 years

The correct answer is (c) 29 years.

Let $f$ be the father’s current age and $s$ be the son’s current age. We know that the ratio of their ages is 7:1, so we can write this as $f = 7s$. We also know that after 4 years, the ratio of their ages will be 4:1. This means that $f + 4 = 4(s + 4)$. Substituting in the first equation, we get $7s + 4 = 4(s + 4)$. Simplifying, we get $3s = 8$. Dividing both sides by 3, we get $s = 8/3$. Substituting this into the first equation, we get $f = 7(8/3) = 28$. Therefore, the sum of their present ages is $f + s = 28 + 8/3 = \boxed{29}$ years.

Option (a) is incorrect because $32$ is not a factor of $28$. Option (b) is incorrect because $35$ is not a factor of $28$. Option (d) is incorrect because $38$ is not a factor of $28$.

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