Question

The sum of the digits of two digit number is $5$. The number obtain by reversing the order of digits diminished the original number by $9$. Find the number.

Answer 1

Let the tens digit $=x$

Let the units digit $=y$

The sum of digits of a two digit number is $5$, so $x+y=5$

When the digits are reversed, the number is $9$ more than the original

since x is your tens digits, its value is $10x$.

So, yo have the value of your original number $10x+y$.

Now, reverse the digits the number $=10y+x$

So, equation formed $=10y+x=(10x+y)=9$

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

$\Rightarrow 9y=9x+9$

$\Rightarrow 9y-9x=9$

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

$\Rightarrow y-x=9/9=1$

$y-x=1$

$y+x=5$

_________

$2y=6$

$\Rightarrow y=6/2$

$\Rightarrow y=3$

Put y in $y-x=1$

$3-x=1$

$-x=1-3$

$x=2$

$\therefore$ The original number is $10x+y=10\left(2\right)+3=20+3=23$.