Question

A number consists of two digits whose sum is $9$. If $27$ is subtracted from the number, its digits are reversed. Find the number.

Answer 1

Let the units digit be $x$.

it is given that, sum of two digits $=9$

$\Rightarrow$ Tens digit $=9-x$

So, the original number $=10\times (9-x)+x$

$=90-10x+x$

Original number $=90-9x$ ---(1)

Now, the digits are interchanged, then

New number $=10x+(9-x)$

New number $=9x+9$ ---(2)

According to the question,

$90-9x-27=9x+9$

$\Rightarrow 63-9x=9x+9$

$\Rightarrow 63-9=9x+9x$

$\Rightarrow 54=18x$

$\Rightarrow \frac{54}{18}=x$

$\Rightarrow 3=x$

Therefore, the number $=90-9x$

$=90-9\left(3\right)$

$=90-27$

$=63$

∴ The number is $63$