Correct Option (C)
To determine the total number of pages, the digits used for numbering are categorized based on the number of digits per page:
- Pages 1 to 9 (single-digit numbers): 9 pages × 1 digit/page = 9 digits.
- Pages 10 to 99 (two-digit numbers): 90 pages × 2 digits/page = 180 digits.
- Pages 100 to 999 (three-digit numbers): 900 pages × 3 digits/page = 2700 digits.
The cumulative digits used for pages 1 to 999 is 9 + 180 + 2700 = 2889 digits.
The remaining digits available for numbering are 3089 (total digits used) - 2889 (digits for pages 1-999) = 200 digits.
These remaining 200 digits are used for four-digit page numbers. The number of four-digit pages is 200 digits / 4 digits/page = 50 pages.
Therefore, the total number of pages in the book is 999 (pages up to three digits) + 50 (four-digit pages) = 1049 pages.
Incorrect Options:
Options (A), (B), and (D) are incorrect. The systematic calculation of digits used for numbering pages, starting from page 1, leads to a unique total of 1049 pages. These alternative options do not align with the correct number of pages derived from the given total digit count of 3089.
