With ratios, it's useful to pick numbers. In this example, it is clear that each statement by itself is not sufficient, so let's take them together.
1) Ratio of filled to unfilled is 5:6. This means the number of total seats is a multiple of 11.
2) Ratio of filled to unfilled is 1:3. This means the number of total seats is also a multiple of 4.
Let's then pick a number for the total number of seats that is a multiple of 11 and 4: 44.
With this number, we now have the following ratios:
1) 20:24 (we multiplied everything by 4 to have a total of 44)
2) 11:33 (we multiplied everything by 11 to have a total of 44)
This means that we had 20 people in the beginning and only 11 in the end, which means that 9 people left. It makes sense: we had 24 unfilled in the beginning and 24+9=33 unfilled in the end, from the 9 that left.
The question asks the ratio of people who watched the entire movie to people who didn't, or 11/9.