Step 1: Understanding the Concept:
Calculate the number of digits used for different ranges of page numbers: 1-digit (1-9), 2-digits (10-99), 3-digits (100-999), and then find how many 4-digit pages are left.
Step 2: Identifying the Vector of Change:
- Pages 1 to 9: $9 \times 1 = 9$ digits.
- Pages 10 to 99: $90 \times 2 = 180$ digits.
- Pages 100 to 999: $900 \times 3 = 2700$ digits.
- Total digits used up to page 999: $9 + 180 + 2700 = 2889$ digits.
Step 3: Calculation:
- Digits remaining for 4-digit pages: $3189 - 2889 = 300$ digits.
- Number of 4-digit pages: $300 / 4 = 75$ pages.
- Total pages: $999 \text{ (previous total)} + 75 = 1074$ pages.
Step 4: Final Answer:
The book has 1074 pages. Thus, the correct option is (b).