Correct Option (B)
To calculate the total number of digits printed for a book containing 150 pages, the pages are categorized by the number of digits required for their numbering:
- Pages 1 to 9: These are 9 pages, each requiring 1 digit. The total digits for this segment are 9 × 1 = 9.
- Pages 10 to 99: These are 90 pages (99 - 10 + 1), each requiring 2 digits. The total digits for this segment are 90 × 2 = 180.
- Pages 100 to 150: These are 51 pages (150 - 100 + 1), each requiring 3 digits. The total digits for this segment are 51 × 3 = 153.
The cumulative sum of digits from all segments is 9 + 180 + 153 = 342.
Incorrect Options:
Options (A) 262, (C) 360, and (D) 450 are incorrect. These values typically arise from errors in segmenting the page ranges, miscalculating the number of pages within a segment, or incorrectly applying the number of digits per page. For example, 450 would be the result if all 150 pages were erroneously assumed to require 3 digits each (150 × 3), which does not account for single-digit and two-digit page numbers.