Question

The number of digits you have to type to write all
the page numbers of a book starting from
1(first page) is 2019. What is the number of pages
in that book?​

Answer 1

Answer:

709

Step-by-step explanation:

For pages 1-9, number of digits = 9 × 1 = 9

For pages 10-99, number of digits = 90 × 2 = 180

Total digits = 189

Remaining = 2019 - 189 = 1830

For pages 100 - 999, the digits required are 3, total digits = 900 × 3 = 2700

but we need to find out the page till digits 1830 only

For Pages 100 - 699, number of digits = 600 × 3 = 1800

Again for the next 10 pages, digits = 10 × 3 = 30

Total digits now = 9 + 180 + 1800 + 30 = 2019

total number of pages in the book = 699 + 10 = 709

Answer 2

Given : The number of digits you have to type to write all the page numbers of a book starting from 1(first page) is 2019

To Find : What is the number of pages in that book?​

Solution:

Number of Digits in 1 Digit number  (1  to 9 ) = 9

Number of digits in 2 digits numbers (10 - 99) = 90 x 2 = 180

Number of digits in 3 digits numbers (100 - 999) = 900 x 3 = 2700   will over pass 2019 and all 3 digit numbers would not be used.

Last page would be a 3 Digit Numbers

Number of Digits used in 3 Digit number = 2019 - 9 - 180

= 1,830

Pages of 3 Digits numbers = 1830/3 = 610

1st 3 digit page is 100 number

Hence 610th 3 digit page would be

Last page = 100 + 610 - 1  = 709

number of pages in that book = 709

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