To find the expected number of students who would like mathematics if 200 more students were asked, we first need to determine the percentage of students who currently like mathematics.
From the data provided, the total number of students surveyed is 100, and the number of students who like mathematics is 10.
The percentage of students who like mathematics can be calculated as follows:
\[ \text{Percentage of students who like mathematics} = \left(\frac{\text{Number of students who like mathematics}}{\text{Total number of students surveyed}}\right) \times 100 \]
\[ \text{Percentage of students who like mathematics} = \left(\frac{10}{100}\right) \times 100 = 10% \]
Now, if we ask 200 more students, we would expect the same percentage to apply.
To find the expected number of students who like mathematics from the new group of 200 students, we calculate:
\[ \text{Expected number of students who like mathematics} = 10% \text{ of } 200 \]
\[ \text{Expected number of students who like mathematics} = 0.10 \times 200 = 20 \]
Therefore, if 200 more students are surveyed, we would expect 20 of them to like mathematics.
The correct answer is 20.