Question

The sum of the digits of a two-digit number is 8. If 18 is added to the value of the number,its digits get reversed. Find the number.

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Answer 1

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

$So, \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ given \: number \Rightarrow10(8-x)+x;$

$\Rightarrow80-10x+x$

$\Rightarrow80-9x$

Now if digits are reversed, then Number obtained,

$\Rightarrow10x+(8-x);$

$\Rightarrow 10x+8-x;$

$\Rightarrow9x+8$

According to question

$\Rightarrow (80 - 9x) + 18 = 9x + 8;$

$\Rightarrow98 - 9x = 9x + 8;$

$\Rightarrow90 = 18x;$

$\Rightarrow \: x = 5$

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

$\Rightarrow80-9 \times 5$

$\Rightarrow80-45 =35$

${ \boxed{ \fbox{the \: number \: is \: 35}}}$