Question

A number is $27$ more than the number obtained by reversing its digits. If its units and tens digits are $x$ and $y$ respectively, write the linear equation representing the above statement.

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 one number is 27 more than the number obtained by reversing its digits, so,

$\left(10y+x\right)-\left(10x+y\right)=27$

$9\left(y-x\right)=27$

$y-x=3$

$x-y+3=0$

So, the required equation is $x-y+3=0$.