A printer numbers the pages of a book starting with 1. He uses 3189 digits in all. How many pages does the book have?

Given:

A printer numbers the pages of a book starting with 1. He uses 3189 digits in all.

To do:

We have to find the number of pages in the book.

Solution:

Number of pages with one digit$=9$    (1 to 9)

Number of pages with two digits$=99-9=90$    (10 to 99)
 Number of pages with three digits$=999-99=900$    (100 to 999)

Let the number of pages with four digits be $x$.

This implies,

$3189=9\times1+90\times2+900\times3+4\times x$

$3189=9+180+2700+4x$

$4x=3189-2889$

$x=\frac{300}{4}$

$x=75$

Total number of pages in the book$=9+90+900+75=1074$.

The total number of pages in the book is 1074.

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Updated on: 10-Oct-2022

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