The pages of book with first page numbered as 1 are printed. Total number of digits printed is equal to 3089. How many pages are there in the book?

Option 2 : 1,049

**Given:**

The pages of book with first page numbered as 1 are printed.

Total number of digits printed = 3089

**Concepts used:**

Number of 1 digit page numbers from 1 to 9 = 9

Number of 2-digits page numbers from 10 to 99 = 90

Number of 3-digit page numbers from 100 to 999 = Sum of number of pages determined using Arithmetic Progression with common difference as 1

**Calculation:**

Number of one-digit number pages = 9

Number of 2-digit number pages = 90

⇒ Number of digits printed from page 1 to page 99 = 9 + (2 × 90) = 189

3-digit numbered pages form an A.P. as difference between consecutive page numbers is always 1.

Let number of pages having 3-digit page number be N.

⇒ 999 = 100 + (N – 1) × 1

⇒ 999 = 99 + N

⇒ N = 900

Sum of digits of 3-digit numbered pages = 3 × 900 = 2,700

⇒ Total number of digits printed using one, two and 3-digit numbers = 189 + 2,700 = 2,889

⇒ Digits left to be printed = 3,089 – 2,889 = 200

⇒ Number of four-digit numbered pages = 200/4 = 50

⇒ Total number of pages = 9 + 90 + 900 + 50 = 1049

**∴**** Book has total of 1,049 pages in all.**