Question

The sum of the digits of a two digit number is $8$ and the difference between the number and that formed by reversing the digits is $18$. Find the number.

Answer 1

Let $x$ be the digit at unit’s place and $y$ be the digit at ten’s place.

Since $y$ is at ten’s place, then the number formed is $10y+x$.

By reversing the digits, it becomes $10x+y$.

As the difference of the numbers is 18, so,

$\left(10y+x\right)-\left(10x+y\right)=18$

$9\left(y-x\right)=18$

$y-x=2$ .... (1)

As the sum of digits is 8, so,

$x+y=8$ .... (2)

On adding equations (1) and (2), we get

$2y=10\Rightarrow y=5$

Putting this in (2), we get $x=8-5=3$

$x=3,y=5$

Hence, number $=10y+x=10\times 5+3=53$.