Question

A two-digit number is such that the sum of its digit is $4$. If $18$ is added to the number, its digits are reversed. Find the number.

Answer 1

Let the number be $10x+y$

According to question, we have,

$x+y=418+10x+y=10y+x$

$\Rightarrow 18+9x=9y$

$\Rightarrow 2+x=y$

$\Rightarrow 2+x=4-x$

$\Rightarrow 2x=2$

$\Rightarrow x=1y=4-x=4-1=3$

Number is $10x+y=10\times 1+3=13$