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If all the $4's$ are replaced by $5,$then sum of all the numbers from $1$ to $100$ wil be equal to$?$
$A)5050$                $B)5090$                        $C)5140$                      $D)5160$
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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.

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