The ratio of ages of a man and his son is 3:After 15 years, the age ratio will be 2:What is the age of the man?

The correct answer is (a).

Let $x$ be the age of the man and $y$ be the age of his son. We are given that the ratio of their ages is 3:1, so $x = 3y$. We are also given that after 15 years, the age ratio will be 2:1, so $(x + 15) = 2(y + 15)$. Substituting $x = 3y$ into this equation, we get $3y + 15 = 2(y + 15)$. Simplifying, we get $y = 15$. Substituting $y = 15$ into $x = 3y$, we get $x = 45$.

Option (b) is incorrect because $40$ is not a multiple of $15$. Option (c) is incorrect because $35$ is not a multiple of $15$. Option (d) is incorrect because $30$ is not a multiple of $15$.