Question

If the number obtained by interchanging the digits of a two digit number is $18$ more than the original number and the sum of the digits is $8$ then what is the original number?

Answer 1

Let the given number be $xy$

$xy$ can be written as $10x+y$

According to the given data

$yx=xy+18$

$\Rightarrow 10y+x=10x+y+18$

$\Rightarrow 9y-9x=18$

$\Rightarrow y-x=2$ ………..$\left(1\right)$

and also its given that sum of digits = 8

$\Rightarrow x+y=8$ ………$\left(2\right)$

Solving equation $\left(1\right)$ & $\left(2\right)$ we get

$x+y=8$

$x-y=-2$

__________________

$2x=6$

$\Rightarrow x=\frac{6}{2}$

$\therefore x=3$ and $y=5$ [from equation(1)]

Hence, the given number is $35$.