Question

The sum of the digits of a two digit number is $8$. If $18$ is added to the number, then the resultant number is equal to the number obtained by reversing the digits of the original number. Find the original number.

Answer 1

Let the number be in the form of $10x+y$, where $x$ and $y$ are the tens digit and the units digit respectively.

Applying the first condition:, we get

$x+y=8$ ....(1)
Applying the second condition, given in the problem
$10x+y+18=10y+x$

$\Rightarrow 9x-9y=-18$
$\Rightarrow x-y=-2$ ....(2)
By solving equations (1) and (2), we get

$x=3$ and $y=5$

Therefore, the number is $35$.