Mr Bob wrote the counting in his notebook from 1 to 10

Question

Mr Bob wrote the counting in his notebook from 1 to 100000. How many times he has written the digit ‘8' while writing the integers from 1 to 100000?

A. 15000
B. 18000
C. 25000
D. 50000
E. 55000

urshi · Accepted Answer

Write all of the numbers as 5-digit numbers.
That is, 00000, 00001, 00002, 00003, .... 99998, 99999

NOTE: Yes, I have started at 00000 and ended at 99999, even though the question asks us to look at the numbers from 1 to 100000. HOWEVER, notice that 000 and 100000 do not have any 8's so the outcome will be the same.

First, there are 100000 integers from 00000 to 99999
There are 5 digits in each integer.
So, there is a TOTAL of 500000 individual digits. (since 100000 x 5 = 500000)

Each of the 10 digits is equally represented, so the 8 will account for 1/10 of all digits.

1/10 of 500000 = 50000

So, there are 50000 0's, 50000 1's, 50000 2's, 50000 3's, . . ., and 50000 9's in the integers from 00000 to 99999

IMO : D

NikuHBS · Answer

Every 100 numbers have any digit written 20 times
Every 1000 numbers have any digit written 300 times
Every 10000 numbers have any digit written 4000 times
Every 100000 numbers have any digit written 50000 times

Option D

monikakumar · Answer

Mr Bob wrote the counting in his notebook from 1 to 100000. How many times he has written the digit ‘8' while writing the integers from 1 to 100000?
A. 15000
B. 18000
C. 25000
D. 50000
E. 55000

counting method also does.
But usual formula to count this can be
n*(10)^n-1
n is the power of 10
5*10^4
50000

Ans D

Spunk17 · Answer

I feel the question is missing additional 0 from 10,000 (it should be 100,000) based on the options. 
8 can be counted using the number of times 8 will come as the single digit, then 8 in the two dights and so on till the 4 digits are counted. 
I believe D would be the answer for the question given here, if we were counting from 1 to 100,000. However, if the count is from 1 to 10000 then the answer is 4000.

MayankSingh · Answer

IMO D

The general formula to calculate any digit in a set of number (From 1 to 10^n) is n×10^n−1

A/C , here n=5

So, no. of 8's = 5x 10^(5-1) = 50000

nothing345 · Answer

Create 5 spaces to place the digits from 0 to 9 as follows: _ _ _ _ _

Start with 0000

Now put 8 in the 100,000s place 8_ _ _ _ this gives us 10,000 possibilities.

Moving on to the next placement of 8 in the 10,000s place we remark something similar: _8_ _ _ 
We again have 10,000 possibilities. Continue this for the next 2 positions and we get: 
10k+10k+10k+10k+10k or 5*10,000 which is equal to 50,000

Hence, Option D is the answer.

YuvarajUmapathi · Answer

Let assume five-place holders.

Fix 8 in the first place holder: 8 __ __ __ __. In the remaining place, we can have numbers from 0-9. So possible numbers are 10*10*10*10 = 10000

Fix 8 in the second place holder: __ 8 __ __ __. In the remaining place, we can have numbers from 0-9. So possible numbers are 10*10*10*10 = 10000

Fix 8 in the third place holder: __ __ 8 __ __. In the remaining place, we can have numbers from 0-9. So possible numbers are 10*10*10*10 = 10000

Fix 8 in the fourth place holder: __ __ __ 8 __. In the remaining place, we can have numbers from 0-9. So possible numbers are 10*10*10*10 = 10000

Fix 8 in the fifth place holder: __ __ __ __ 8. In the remaining place, we can have numbers from 0-9. So possible numbers are 10*10*10*10 = 10000.

Total possible numbers = 10000 * 5 = 50000

Saasingh · Answer

OA D?

Uptil 100,000 we have

NOTE : repetition allowed while counting

_ 1 digit number 
==== 1 way

_ _ 2 digit number 
==== 10+9 = 19 ways

_ _ _ 3 digit number 
==== 100+90+90 = 280

_ _ _ _ 4 digit number 
==== 1000+900+900+900 = 3700

_ _ _ _ _ 5 digit number 
==== 10000+9000+9000+9000+9000 = 46000

Adding all we get 50,000.

Posted from my mobile device

ArunSharma12 · Answer

consider the following cases:
single digit: one time 8 will be written: 1

two digits: 
case 1: unit digit is 8, other digits can be filled in 9 ways: 9; numbers will be from 1-9
case 2: ten digit is 8, other digits can be filled in 10 ways: 10
total = 19

three digits:
case 1: unit digit is 8, other digits can be filled in 9*10 ways: 90
case 2: tens digit is 8, other digits can be filled in 9*10 ways: 90
case 3: hundreds digit is 8, other digits can be filled in 10*10 ways: 100
total = 280

four digits:
case 1: unit digit is 8, other digits can be filled in 9*10*10 = 900
case 2: tens digit is 8, other digits can be filled in 9*10*10 = 900
case 3: hundreds digit is 8, other digits can be filled in 9*10*10 = 900
case 4: thousands digit is 8, other digits can be filled in 10*10*10 = 1000
total = 3700

five digits:
case 1: unit digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 2: tens digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 3: hundreds digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 4: thousands digit is 8, other digits can be filled in 9*10*10*10 = 9000
case 5: ten thousands digit is 8, other digits can be filled in 10*10*10*10 = 10000

total = 46000 + 3700 + 280 + 19 + 1 = 50000
Ans: D

aggvipul · Answer

All 5 digit no.s from 1 to 100000 are between 00000 to 99999 
taken 00000 and 99999 because anyways, no. 8 won't be present in in 1 or in 100000.

There are 100000 integers from 00000 and 99999
so far so good, there are 5 digits in each integer therefore there are a total of = 5*100000 = 500000 digits
Since each of the 10 digits(0 to 9) is equally represented, so no. 8 will account for 1/10 of all the digits, therefore=  \frac{500000*1}{10} 
 That is no. 8 would be represented 50000 times

Hit Kudos

ashwini2k6jha · Answer

ANSWER:D
 Number of 8 in 1-100 =10+10=20 (number in 80-89=10 and number in 8,18,28...98=10)
Number of 8 in 1-1000=100 +(20x10)=300 (number in 10s 100=20x10 and number in 800-899=100)
Number of 8 in 1-10000=1000+(300x10)=4000 (number in 10s 1000=300x10 and number in 8000-8999=1000)
Number of 8 in 1-100000=10000+(4000x10)=50000 (number in 10s 10000=4000x10 and number in 80000-89999=10000)

Archit3110 · Answer

for digits from 1 to 1,00,000 ; 5 digits per number will be used we have
5*10^5 and total digits are 10 ; 
so only digit 8 will come 5*10^5/10 ; 5*10^4
OPTION D

Mr Bob wrote the counting in his notebook from 1 to 100000. How many times he has written the digit ‘8' while writing the integers from 1 to 100000?
A. 15000
B. 18000
C. 25000
D. 50000
E. 55000

bumpbot · Answer

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Mr Bob wrote the counting in his notebook from 1 to 10

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