Number System
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Q.

A boy writes all the numbers from 100 to 999. The number of zeroes that he uses is '$a$', the number of 5's that he uses is '$b$' and the number of 8's he uses is '$c$'.

What is the value of $b+c-a$?

 A.

280

 B.

380

 C.

180

 D.

80

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Solution:
Option(B) is correct

We can see by symmetry $b=c$ and hence all we need to calculate $b$ and $a$

$b= 280\text{ and }a= 180$

⇒ $2b-a =$ 380

Edit: For an alterntive solution, check comment by Abdulkhader.

Edit 2: For yet another alternative solution, check comment by Sravan Reddy.


(7) Comment(s)


Sravan Reddy
 ()

I think it better to memorize few things for quick calculations

From 1 to 99, each number will be used $20$ times (Exception: 0 - only 10 times as we do not count zeros for 00,01,02,03.....09. Else it would also be 20)

If we remember the value 20, then coming to the problem. There are total 9 (00,99) sets in 100 to 999.

number of zero's $= 20*9 = 180$

Number of 5's/8's $= 20*9 + 100 = 280$ (100 is for the 100's digit)

$b+c-a = 280+280-180 = 380$



Abdulkhader
 ()

if we think , then the numbers like 100, 200 300 are 9 in total then the zeroes in them are 9*2=18

now if we see numbers like 101 ,102, 103,201 are 9 in each set of 100 numbers. then in 9 sets the total zeroes are 9*9=81

then we come to numbers like 110 120 920 etc . so these numbers are 9 in each set of hundred then we have total zeroes are 9*9=81,

then in total number of zeroes are 81+81+18=180

now to count 5

if we conlude a number in ones place, are 105 205 125etc 10 per set so total are 9*10=90

5's in tens place lik 150 151 159 are 10 in each set so 10*9=90

now 5 in hundred place are fromm 500-599= 100 , so the total is 100+90+90=280

from this the the equation will be (2*280)-180=380



Sweety Kumari
 ()

how result came 380.....since no of 0, 5, and 8 is 160,160 1nd 160.


Shivendra Mohan Shukla
 ()

@sweety kumari,

try to solve logically..... count all 0's from 100 -199, and use symmetry upto 999.

Shivendra Mohan Shukla
 ()

@sweety kumari,

try to solve logically..... count all 0's from 100 -199, and use symmetry upto 999.


Shivendra Mohan Shukla
 ()

Smiletry to solve it......