Question

If the sum of two digit number and the number obtained by reversing, the digit is $99$. If the digits of the number differ by $5$, find the numbers.

Answer 1

Let the two digit number be $10x+y$

$x-y=5$

$x=5+y$ (1)

Also $10x+y+10y+x=99$

$11x+11y=99$

$x+y=9$ (2)

Substituting (1) in (2)

$5+2y=9$

$2y=4$

$y=2$ (3)

Substituting (3) in (1) gives $x=7$

Hence the numbers are $72$ and $27$