10. It is known that someone bought a car for 121,000 yuan. If the annual insurance, maintenance, and gasoline costs total 10,000 yuan, and the car repair costs are 0 yuan in the first year, and from the second year onwards, increase by 0.2 ten thousand yuan each year. Then, after using the car for $\qquad$ years, it should be scrapped to minimize the annual average cost of the car, and the minimum annual average cost of the car is $\qquad$ ten thousand yuan.
$10.11,3.1$.
After using the car for $x$ years, the annual average cost is
$$
\begin{array}{l}
y=\frac{1}{x}\left\{12.1+x \times 1+\frac{x}{2}[0+0.2(x-1)]\right\} \\
=0.9+0.1 x+\frac{12.1}{x} \\
\geq 0.9+2 \sqrt{0.1 \times 12.1}=3.1 .
\end{array}
$$

The minimum annual average cost of the car is 3.1 ten thousand yuan, which occurs if and only if $0.1 x=\frac{12.1}{x}$, i.e., $x=11$ (years).
(Xia Xingtu and Chen Chuanli provided)