A book has 300 pages in all. How many digits have been used to write the page numbers from 1 to 300?
a)1192
b)792
c)900
d)700
0 . 0 answers . 1 day ago
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Answers
900
c
Step-by-step explanation:
1-300
300 pages+300digits=600
600=300over all pages
Answer:
There were 792 digits used in all of 300 pages.
Option b. is correct.
Step-by-step explanation:
We have,
A book with 300 pages
Now,
Total digits used = Total No. of 1 digit numbers + Total No. of 2 digit numbers + Total No. of 3 digit numbers
Page having 1 digit number = 1, 2, 3,......, 9
Now,
No. of pages from 1 to 9 = (9 - 1) + 1
= 9
Similarly,
Pages having 2 digit numbers = 10, 11,....98, 99
Then,
No. of pages from 10 to 99 = (99 - 10) + 1
= 90
Also,
Pages having 3 digit numbers = 100, 101,....., 299, 300.
Then,
No. of pages from 100 to 300 = (300 - 100) + 1
= 201
Now, we have,
No. of pages having 1 digit number = 9 pages
No. of pages having 2 digit numbers = 90 pages
No. of pages having 3 digit numbers = 201 pages
We can also check this,
Total pages = 300
Now,
201 + 90 + 9 = 300
Hence, it is correct.
Now,
There is only 1 digit used in the First 9 pages,
So,
Digits used = (1 × 9) = 9
Similarly,
There are 2 digit numbers used in 90 pages,
So,
Digits used = (2 × 90) = 180
Also,
There are 3 digit numbers used in 201 pages
So,
Digits used = (3 × 201) = 603
Thus,
Total digits used = Total No. of 1 digit numbers + Total No. of 2 digit numbers + Total No. of 3 digit numbers
Total digits used in 300 pages
= 9 + 180 + 603
= 792 digits
Hence,
There were 792 digits used in all of 300 pages.
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