Question

$abc$ is a three-digit number. This three-digit number is reversed and subtracted from the original number. By which number will the difference obtained be always divisible?

Answer 1

Here, $abc$ is a 3-digit number.
General form of $abc$ will be
100$a$ + 10$b$ + $c$
Number obtained by reversing the digits of abc is $cba$.
General form of $cba$ will be
100$c$ + 10$b$ + $a$
The difference between the original number and reverse number is
$abc-cba$
$=(100a+10b+c)-(100c+10b+a)$
$\Rightarrow abc-cba=99(a-c)$
$\Rightarrow abc-cba=9\times 11(a-c)$

Hence, the difference is divisible by 9 as well as 11.

So, option (c) is correct.