Question

A no. is $27$ more than the no. obtained by reversing its digit. If its unit and tens digit are $X$ and $Y$ respectively. Write the linear equation representing the above statement.

Answer 1

Let unit digit be $x$

and, tens digit be $y$

Then

The number$=10x+y$

and

Reversing number $=10y+x$

And according to question,we get

$\begin{array}{c}10x+y=10y+x+27\\ \Rightarrow 10x+y-10y-x=27\\ \Rightarrow 9x-9y=27\\ \Rightarrow 9\left(x-y\right)=27\\ \Rightarrow x-y=\frac{27}{9}\\ \Rightarrow x-y=3\end{array}$

Which is a linear equation.