Question

The sum of digits of a two digit number is $9$. If $27$ is subtracted from the
number, the digits are reversed. Find the number.

Answer 1

Let us assume, $x$ and $y$ are the two digits of the two-digit number

Therefore, the two-digit number $=10x+y$ and

Reversed number $=10y+x$

Given:

$x+y=9$ ......(1)

Also given:

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

$9x-9y=27$

$x-y=3$ ......(2)

Adding equation (1) and equation (2)

$2x=12$

$x=6$

Hence,

The two-digit number $=10x+y\Rightarrow 10\times 6+3=63.$