Question

The sum of the digits of two digit number is $3$. The number obtained by interchanging the digit is $9$ less than the original number. Find the original number.

Answer 1

Let the unit digit be $x$ , then tens place digit will be $3-x$

So, the given number = $x+10(3-x)$

= $x+30-10x$

= $30-9x$

If digits are interchanged , then the number obtained = $10x+3-x$

= $9x+3$

According to question

$9x+3$ = $30-9x-9$

$\Rightarrow$$18x=18$

$\Rightarrow$ $x=1$

So , $3-x$ $=3-1=2$

Hence the required number is $21$