100 * 101 /2 +(110)

= 50*99 +110 = 5160

The Gateway to Computer Science Excellence

+5 votes

If all the $4's$ are replaced by $5,$then sum of all the numbers from $1$ to $100$ wil be equal to$?$

$A)5050$ $B)5090$ $C)5140$ $D)5160$

$A)5050$ $B)5090$ $C)5140$ $D)5160$

0

@Anu007 I am getting 109 extra..can you please tell me where am I missing out..

4->5,14->15,24->25,34->35,54->55...94->95 such cases are 9.

Then for 40->50 to 43->53 and 46->56 to 49->59 has an increment of 10. 8 such cases. So 8*10=80.

44->55 has 11 increment and 45->54 has 9. So 20.

Total cases coming as 9+80+20=109.

What is the 110th one?

4->5,14->15,24->25,34->35,54->55...94->95 such cases are 9.

Then for 40->50 to 43->53 and 46->56 to 49->59 has an increment of 10. 8 such cases. So 8*10=80.

44->55 has 11 increment and 45->54 has 9. So 20.

Total cases coming as 9+80+20=109.

What is the 110th one?

+2

10 places 1 is increase and 10 places 10 increase from 40 =50, 41= 51 ....etc till 49= 59. 10 +100 = 110.

As said by @joshi_nitish and @ravi

As said by @joshi_nitish and @ravi

+1

@ MiNiPanda Your step $45\rightarrow 54$ is bit wrong , $\color{blue}{45\rightarrow55} $ is what question mentioned.

+4 votes

Best answer

Total numbers with $4$ as their unit place : $10$ $\{4,14,24,34,44,54,64,74,84,94 \}$

Total numbers with $4$ as their tens' place :$10$ $\{40,41,42,43,44,45,46,47,48,49 \}$

Sum of $100$ numbers without updation : $\Large \frac{100 \times 101}{2} $ $=5050$

Every unit place will increment the sum by $1$ and tens' place by $10$.

$\therefore $ Total incremented value = $10 \times 10 + 10 \times 1 =110$

Complete Sum = $\color{Red}{5160}$

Footer note :

$44$ is special case here so if i mentioned in both set,though it can be tackled separately but gist will be same like :

$\Rightarrow $ First treat it as Row element of $40$ then increment is as $\color{Red}54$

$\Rightarrow $ Now as unit place element then increment is as $\color{Red}{55}$

But overall change is $55-44=11$ same like above calculation.

0

Unit place: 04 , 14 , 24 , 34 , 44 , 54 , 64 , 74 , 84 , 94(Total = 10)

replaced by: 05 , 15 , 25 , 35 , 45 , 55 , 65 , 75 , 85 , 95 (Each increase by one so 10*1 = 10)

and

tense place: 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49(Total = 10)

replace by : 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 ( Each increase by 10th so 10*10 = 100)

So total =10 + 100 = 110

final answer is 5050 + 110 = 5160

replaced by: 05 , 15 , 25 , 35 , 45 , 55 , 65 , 75 , 85 , 95 (Each increase by one so 10*1 = 10)

and

tense place: 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49(Total = 10)

replace by : 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 ( Each increase by 10th so 10*10 = 100)

So total =10 + 100 = 110

final answer is 5050 + 110 = 5160

52,218 questions

59,888 answers

201,081 comments

118,127 users