Question

Sum of the digits of a two digit number is 5 and difference of the digits is 1. Also, the tens place is greater than the unit place digit. The number is .

Answer 1

Let the number be represented as $xy.$
$\therefore x+y=5...\left(a\right)$
As the tens place digit is greater than the unit place digit,
$x-y=1...\left(b\right)$

To eliminate $y,$ add $\left(a\right)$ with $\left(b\right).$
$x+y+x-y=5+1$
$\Rightarrow 2x=6$
$\Rightarrow x=3$
Substituting $x$ in $\left(a\right)$ we get,
$3+y=5$
$\Rightarrow y=2$
$\therefore$ The number $xy$ is $32.$