The easiest way to solve this is to think about the number of times the digit 1 appears in each decimal place (ie, ones, tens, etc).
Assuming the pages are numbered 1-500, then the digit 1 will appear in the ones place on page 1, 11, 21, … and so on, up to 491. So, every 10 consecutive integers, the digit 1 is in the ones place exactly once. To be more precise, it appears in 50 ones places.
The digit 1 will appear in the tens place on pages 10,11, …, 19, 110, 111, …, 119, and so on. So in every 100 consecutive integers, the digit 1 is in the tens place exactly 10 times. If you count, it appears 50 times.
Finally, the digit will appear in the hundreds place from pages 100-199, which is 100 pages.
So the digit 1 appears 200 times.
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