Question

The sum of the digits of $2-$digit number is $12$. If the number formed by reversing the digits is less than the original number by $54$, find the original number.

Answer 1

Let $2$ digit number $=ab$

$a+b=12$ ………$\left(1\right)$

$(10a+b)-(10b+a)=54$

$9a-9b=54$

$a-b=6$ ……….$\left(2\right)$

from $\left(1\right)$ & $\left(2\right)$

$a+b=12$

$a-b=6$

$(+)$

_____________

$a=9$

_____________

$a+b=12$

$a+b=12$

$b=3$

$\therefore$ Original number $=93$.