Question

The sum of the digits of a two-digit number is 9. If 9 is added to the number formed by reversing the digits, then the result is thrice the original number. Find the original number.

Answer 1

Let the two digit number be $xy$

$x+y=9$

$yx+9=3\left(xy\right)$

$10y+x+9=3(10x+y)$

$x+10y+9=30x+3y$

$29x=7y+9$

$y=9-x$

$29x=7(9-x)+9$

$36x=63+9$

$36x=72$

$x=2$

$x+y=9$

$y=9-2=7$

Original number $=27$