Question

A number consists of two digits whose sum is $8$. If $35$ is added to the number its digits are reversed. Find the number.

Answer 1

Let one digit of the number be $x$ , then its ten digits digits will be $(8-x)$ .

So , given number $=10\left(8-x\right)+x$

$=80-10x+x$

$=80-9x$

Now if digits are reversed , then Number obtained

$=10x+\left(8-x\right)$

$=10x+8-x$

$=9x+8$

According to question

$\left(80-9x\right)+18=9x+8$

$98-9x=9x+8$

$90=18x$

$x=5$

$\Rightarrow$ given number $=80-9x$

$=80-9\times 5$

$=80-45$

$=35$

$\therefore$ the number is $35$