A mother tells his daughter 'I was half your present age when you were born'. If the mother is $18$ years older than her daughter, what is the present age of the mother ?

Let the daughter's present age be $x$ years. The mother was half of this, or $x/2$ years old, when the daughter was born. Therefore the age difference between mother and daughter is $x - x/2 = x/2$ years. Since the mother is 18 years older, $x/2 = 18$, meaning $x = 36$ is the daughter's current age. Adding 18 to 36 gives the mother's present age as 54 years.

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