Question

The sum of the digits of a 2-digit number is 0. If we reverse the digit, the new number will be 54 more than the original number, what is the original number?

Answer 1

Consider that the digits are $a$ and $b$.

The original number is $10a+b$

The reversed number is:

$a+10b$

Now,

$a+b=10$

$(a+10b)-(10a+b)=54$

This implies that:

$54=9b-9a=9(b-a)$

Hence,

$b-a=549=6$, so $4b=a+6$

This implies that:

$a+a+6=10$

Hence, $a=2,b=8$ and the original number was $28$