Question

The sum of the digits of a two digit number is $15$. If $9$ is added to the number, the digit are reversed. Find the number.

Answer 1

Suppose the digit is $xy$ then

$x+y=15$ (Given)

$x=15-y$ ......(1)

Multiplying by $x$ both sides

and

$xy+9=yx$ (Given)

Or

$10y+x=9+(10x+y)$

$9y=9x+9$

On substituting the value of $x$, we get

$9y=135-9y+9$

$18y=144$

$y=8$,

So,

$x=15-y=15-8=7$

Hence, the number is $x=78.$