Question

The total number of digits used in numbering the pages of a book having $366$ pages is

• A. $732$
• B. $850$
• C. $990$
• D. $1305$

Answer 1

The correct option is C

$990$

Step 1: The explanation for the correct options:

Given : Total number of pages = $366$.

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{digits}=\mathrm{Number}\mathrm{of}\mathrm{digits}\mathrm{in}1-\mathrm{digit}\mathrm{page}\mathrm{numbers}+ \\ \mathrm{Number}\mathrm{of}\mathrm{digits}\mathrm{in}2-\mathrm{digit}\mathrm{page}\mathrm{numbers}+\mathrm{Number}\mathrm{of}\mathrm{digits}\mathrm{in}3 \\ -\mathrm{digit}\mathrm{page}\mathrm{numbers} \end{gathered}$$

$=(1\times 9+2\times 90+3\times 267)$

$=(9+180+801)$

$=990.$

Therefore, the total number of digits used in numbering the pages of a book having $366$pages is $990.$.

Step 2 : The explanation for the incorrect options:

Option (A):

$\bullet$The number$732$ does not match with the arrived result which is $990.$.

$\bullet$Hence the incorrect option is (A)

Option (B):

$\bullet$Arrived result does not match with the given number in the statement of the problem.

$\bullet$Hence the incorrect option is (B).

Option (D):

$\bullet$Number $1305$does not match with the arrived result.

$\bullet$Hence the incorrect option is (D).

Therefore, The correct option is (B).