Question

The sum of the two digits of a $2-$digit number is $9$. When the digits are reversed, the number deceases by $9$. Find the original number.

Answer 1

Let the two digit number be $10x+y$

$x+y=9$

$x=9-y$ (1)

Also $10x+y=10y+x+9$ (2)

Substituting (1) in (2)

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

$90-10y+y=9y+18$

$72=18y$

$y=4$ (3)

Substituting (3) in (1) gives

$x=5$

Hence the number is $54$