Question

The sum of digits of a two digit number is $15$. The number obtained by reversing the order of digits of the given number exceeds the given number by $9$. Find the given number.

Answer 1

Let the tens,unit digit of number be$=x,y$ respectively

Here $xy=10x+y$

$\Rightarrow x+y=15$

Second condition :

$\Rightarrow 10y+x=9+10x+y$

$\Rightarrow 9x-9y=-9$

$\Rightarrow x-y=-1$

Add resultant equations ;

$\Rightarrow 2x=14$

$\Rightarrow x=7$

$\Rightarrow y=8$

$\therefore$two digit number $=78$