Find the sum of all the digits of the result of the subtraction $10^{99} - 99$ .

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Solution

$1000000..............0000$
$- 99$
.............................................
$99999...................9901$
............................................
The result is a $99$ digit number having $97$ nines followed by a zero and $1$ .
$∴$ The sum of the digits $= (97 \times 9) + 0 + 1$
$= 874$

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Find the sum of all the digits of the result of the subtraction 1099−99.

1000000..............0000 −99.............................................99999...................9901............................................The result is a 99 digit number having 97 nines followed by a zero and 1.∴ The sum of the digits =(97×9)+0+1=874

Find the sum of all the digits of the result of the subtraction $10^{99} - 99$ .

$1000000..............0000$
$- 99$
.............................................
$99999...................9901$
............................................
The result is a $99$ digit number having $97$ nines followed by a zero and $1$ .
$∴$ The sum of the digits $= (97 \times 9) + 0 + 1$
$= 874$