'ABC' is a 3 digit number if it is reversed then the sum of digits of the difference between the original and the reversed number will always be divisible by:

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Solution

The correct option is D
All of these

ABC can be written as $100 A + 10 B + C$

Similarly CBA can be written as
$100 C + 10 B + A$
$A B C - C B A = (100 A + 10 B + C) - (100 C + 10 B + A)$
$= 100 A + 10 B + C - 100 C - 10 B - A$
$= 99 (A - C)$
$= 9 \times 11 (A - C) = 3 \times 3 \times 11 (A - C)$
This number is divisible by 3,9,11 and 99.
If a number is divisible by 9 and 3, the sum of the digits of that number must be divisible by 9 and 3 respectively.

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