The difference beween a 3-digit number ABC and the number obtained by interchanging it's digits is always divisible by:

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Solution

The correct option is A 99
The 3-digit number ABC can be written as 100A + 10B + C

Similarly CBA can be written as:
100C + 10B + A

Difference
= (100A + 10B + C) - (100C + 10B + A)
= 100A + 10B + C - 100C - 10B - A
= 99 (A - C)

$= 9 \times 11 (A - C) = 3 \times 3 \times 11 (A - C)$

This number is divisible by only 3 ,9, 11 and 99.

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