Its not impolite to ask ages in China, especially for old generations. There are several ways to phrase the question. You can say '你多大了(nǐ duō dà le ？)？' or '你几岁了(nǐ jǐ suì le)？'
If you are 20 years old, you can answer it by saying 我二十岁 - wǒ èr shí suì
岁 (suì ) means age, or years old.