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1. 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?

A. 32 years

B. 36 years

C. 40 years

D. 48 years

Solution:

\begin{aligned} Let the mother's present age be x years . \\ Then, the person's present age \\ = \frac{2}{5} x years \\ ∴ \frac{2}{5} x + 8 = \frac{1}{2} (x + 8) \\ \Rightarrow 2 (2 x + 40) = 5 (x + 8) \\ \Rightarrow x = 40 \end{aligned}

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