A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?

Explanation:-

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{mother's}}\,{\text{present}}\,{\text{age}}\,{\text{be}}\,x\,{\text{years}}{\text{.}} \cr & {\text{Then,}}\,{\text{the}}\,{\text{person's}}\,{\text{present}}\,{\text{age}} \cr & = \left( {\frac{2}{5}x} \right)\,{\text{years}} \cr & \therefore \left( {\frac{2}{5}x + 8} \right) = \frac{1}{2}\left( {x + 8} \right) \cr & \Rightarrow 2\left( {2x + 40} \right) = 5\left( {x + 8} \right) \cr & \Rightarrow x = 40 \cr}$$