Age Problem

Ann's age at THAT particular time was $\dfrac{1}{2}$ of Mary's CURRENT age. Now note that the difference between Mary's age now and at THAT particular time is the same as the difference between Ann's age now and at THAT particular time. Considering that Mary's age at THAT particular time is the same as Ann's age NOW , this common age must be $\dfrac{1}{2}+\dfrac{1}{2}\dfrac{1}{2}=\dfrac{2+1}{2\times 2}=\dfrac{3}{4}$ of Mary's CURRENT age, which is $\dfrac{3}{4} \times 24=3\times 6=\boxed{18}$ .