Question

The sum of the digits of two-digit number is $13$. The number obtained by interchanging its digits exceeds the given number by $9$. Find the original number.

Answer 1

Number $=y\times 10+x$

$x+y=13\Rightarrow y=13-x$

Interchange digits.

$x\times 10+y=$ Number $+9$

$x\times 10+13-x=(13-x)\times 10+x+9$

$10x+13-x-130+10x-x-9=0$

$18x=126$

$x=7$

$y=6$

Number $=60+7=67$