10. (10 points) Xiao Ming and Xiao Hua are in Class 6 (1), which has between 20 and 30 students, and each student has a unique birthday. Xiao Ming says: “The number of students older than me is twice the number of students younger than me.” Xiao Hua says: “The number of students older than me is three times the number of students younger than me.” How many students are in this class?
【Analysis】Let the number of students younger than Xiao Ming be $x$, and the number of students younger than Xiao Hua be $y$. Then the number of students older than Xiao Ming is $2x$ people, so the total number of students in the class is $N=3x+1$ people. Also, because the number of students older than Xiao Hua is $3y$ people, the total number of students in the class is $N=4y+1$ people. Therefore, $\mathbf{N}-1$ is a multiple of both 3 and 4, so $\mathbf{N}-1$ is a multiple of $3 \times 4=12$. Given that the number of students in the class is between 15 and 30, $\mathbf{N}-1$ can only be 24, so the class has a total of $N=24+1=25$ students.
【Solution】Solution: From the analysis, let the number of students younger than Xiao Ming be $x$, and the number of students younger than Xiao Hua be $y$. Then the number of students older than Xiao Ming is $2x$ people, so the total number of students in the class is $N=3x+1$ people. Also, because the number of students older than Xiao Hua is $3y$ people, the total number of students in the class is $N=4y+1$ people. Therefore, $\mathbf{N}-1$ is a multiple of both 3 and 4, so $\mathbf{N}-1$ is a multiple of $3 \times 4=12$.

Given that the number of students in the class is between 20 and 30, $\mathbf{N}-1$ can only be 24, so the class has a total of $N=24+1=25$ students.

Answer: The class has 25 students.