12. (5 points) When Grandpa's age was 2 times Dad's age, Xiaoming was 1 year old; when Dad's age was 8 times Xiaoming's age, Grandpa was 61 years old. Then, Grandpa is $\qquad$ years older than Xiaoming; when Grandpa's age is 20 times Xiaoming's age, Dad's age is $\qquad$ years.
【Solution】Solution: (1) Let the grandfather be $x$ years older than Xiaoming, according to the problem, we can get the equation:
$$
x+1-\frac{\mathrm{x}+1}{2}=61-8 \times(61-x),
$$

After rearranging, we get: $15 x=855$,
$$
x=57,
$$
(2) When Xiaoming was 1 year old, the grandfather's age was: $57+1=58$ (years old), and the father's age was: $58 \div 2=29$ (years old); so the age difference between the grandfather and the father is: $58-29=29$ (years), and the age difference between the father and Xiaoming is: $29-1=28$ (years). Let the father's age be $y$ years when the grandfather's age is 20 times that of Xiaoming, according to the problem, we can get the equation:
$$
\begin{aligned}
29+y & =20 \times(y-28), \\
19 y & =589, \\
y & =31,
\end{aligned}
$$

Answer: The grandfather is 57 years older than Xiaoming; when the grandfather's age is 20 times that of Xiaoming, the father's age is 31 years old. Therefore, the answers are: $57 ; 31$.