11. This year, Grandfather's age is 6 times Xiaoming's age. In a few years, Grandfather's age will be 5 times Xiaoming's age. A few years later, Grandfather's age will be 4 times Xiaoming's age. Find: How old is Grandfather this year?
11.【Solution】Grandfather's age is greater than Xiaoming's age, and the age difference between the two is constant.
Since Grandfather's age this year is 6 times Xiaoming's age.
Therefore, the age difference is 5 times Xiaoming's age, which means the age difference is a multiple of 5.
Similarly, from “a few years later, Grandfather's age is 5 times Xiaoming's age” and “after a few more years, Grandfather's age is 4 times Xiaoming's age”, we know that the age difference is a multiple of 4 and 3, so the age difference is: $5 \times 4 \times 3=60$ times. The multiples of 60 are: $60, 120, \cdots$, a reasonable choice is 60, thus, Xiaoming's age this year is $60 \div 5=12$ (years old), and Grandfather's age is $12 \times 6=72$ (years old).
Answer: Grandfather is 72 years old this year.
【Another Solution】Let Xiaoming be $x$ years old this year, then Grandfather is $6 x$ years old this year. $y$ years later, Grandfather's age is 5 times Xiaoming's age, so $5(x+y)=6 x+y$ which means $x=4 y$, and after another $z$ years, Grandfather's age is 4 times Xiaoming's age,
so $4(x+y+z)=6 x+y+z$ which means $2 x=3 y+3 z$
$\because$ Grandfather is $6 x$ years old this year,
$$
\begin{array}{l}
\therefore 6 x \leqslant 100 \quad x \leqslant \frac{50}{3}=16 \frac{2}{3} \\
\text { Also } \because x=4 y \quad \therefore x \geqslant 4
\end{array}
$$

From $4 \leqslant x \leqslant 16 \frac{2}{3}$ and $x=4 y$, we know that $x$ could be $4, 8, 12, 16$.
Also from $2 x=3 y+3 z$, i.e., $y+z=\frac{2}{3} x$, we know that $x$ is a multiple of 3, so $x=12$, thus $6 x=72$.