A book is numbered using consecutive natural numbers starting with 1. if the number of digits used for numbering the first half of the book is exactly 100 less than the number of digits used for numbering the second half, how many pages does the book have ?

• 190 pages are there.
  
• 12 years agoHelpfull: Yes(5) No(1)
• Book Have totally 190 Pages.
  
  It means Half of the Book Having = 190/2 = 95Pages.
  
  For First 1-95 pages, we use 181 digits.
  (i.e)
  -->Between 1-9pages = 9 pages = 9*1 =9 digits used
  -->Between 10-95 pages = 86 pages = 86 *2 = 172 digits used
  -->Totally, we use 172+9 = 181 digits is used for first half of the pages.
  
  For Second half of the book, 96-190 pages, we use 281 digits
  (i.e)
  -->Between 96-99 pages = 4 pages = 4 *2 digits = 8 digits used.
  -->Between 100-190 pages = 91 pages = 91 *3 digits = 273 digits used.
  -->Totally, we use 273+8 = 281 digits used for second half of the book.
  
  That means, exactly 100 less than total number of digits used in first half than the Second half. (281 digits - 181 digits = 100 digits)
• 12 years agoHelpfull: Yes(1) No(6)