The sum of digits of a two-digit number is 8. If 36 is added to the number then the digits reversed. Find the number.

Given :

The sum of the digits of a two-digit number is 8, if 36 is added to the number the digits get reversed.

To find :

We have to find the number.

Solution :

Let the number be $10x+y$.

$x+y=8$

It is also given that if 36 is added to the number the digits gets reversed.

Therefore,

$10x+y+36 = 10y+x$

$10y+x-10x-y = 36$

$10y-y+x-10x= 36$

$9y-x(10-1)=36$

$9y-9x=36$

$9(y-x)=36$

$y-x=\frac{36}{9}$

$y-x=4$

$y-x=4$ and $x+y=8$

Adding them,

$y-x+x+y=4+8$

$2y=12$

$y=\frac{12}{2}$

$y=6$

$x+6=8$

$x=8-6$

$x=2$

The original number is $10(2)+6=20+6=26$.

Therefore, the number is 26.