Question

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

Answer 1

There are $9$ one digits $=9$

There are $90$ $2$ digits $\Rightarrow 90\times 2=180$

There are $900$ $3$ digits $\Rightarrow 900\times 3=2700$

Let there be 'x' $4$ digit numbers.

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

$4x+189=489$

$4x=300$

$x=75$

$999+75=1074$

Hence there are $1074$ pages is all.