A man is 42 years old and his son is 12 years old. In how many years will the age of the son be half the age of the man at that time?

The age of man = 42 years

The age of son = 12 years

Let the son's age be half of the man's age after x years.

Son's age + x = $\dfrac{1}{2}$ (Man's age + x)

⇒ 12 + x = $\dfrac{1}{2}$ (42 + x)

⇒ 2 $\times$ (12 + x) = 1 $\times$ (42 + x)

⇒ 24 + 2x = 42 + x

⇒ 2x - x = 42 - 24

⇒ x = 18

Hence, after 18 years, the son's age will be half of the man's age.