Question

The sum of digits of a two-digit number is $9$. If $27$ is subtracted from the number, the digits change their places. Find the number.

Answer 1

Let the two-digit no. is $xy$

Given that $xy-27=yx$

It can be written as

$10x+y-27=10y+x$

$9x=9y+27$

$x-y=3\to 1$

Given that $x+y=9\to 2$

Adding both equations $1+2$

$2x=12$

$x=6,y=3$

$\therefore$ No. is $xy=63$