Question

What is the total number of digits used in numbering the

pages of a book having 456 pages?


1:) 1260

2:) 1290

3:) 1350

4:) 2550​

Answer 1

$\large\underline{\text{Solution}}$

We assume that the pages start from 1.

A one-digit number is greater or equal to 1 and less than 10.

$\implies10-1=9$

There are 9 possible one-digit numbers.

A two-digit number is greater or equal to 10 and less than 100.

$\implies100-10=90$

There are 90 possible two-digit numbers.

A three-digit number is greater or equal to 100 and less than 1000. However, we have 456 at the last page.

$\implies456-100=356$

Then we have 356 possible three-digit numbers.

The total digit will be the sum of

$\rightarrow\text{The number of one-digit number}\times1$

$\rightarrow\text{The number of two-digit number}\times2$

$\rightarrow\text{The number of three-digit number}\times3$

$\text{(Total number of digits)}$

$=9\times1+90\times2+356\times3$

$=9+180+1068$

$=1257$

$\large\underline{\text{Answer}}$

None of the above is correct.

Answer 2

Given :  a book having 456 pages

To Find :   total number of digits used in numbering

Solution:

a book having 456 pages

9 number with single digits

90 numbers with 2 Digits

remaining 456 - (9 + 90) = 357 pages with 3 Digits

Total Digits =

9 * 1  + 90 *2  + 357 * 3

= 9 + 180 + 1071

= 1260

Hence  total number of digits used in numbering the  pages of a book having 456 pages are 1260

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