What a number!

list all possible solution that can obtain the answer of nine. then we get 81, 72, 63, and 54. then interchange and deduct. 81-18=63. 72-27=45. 63-36=27. 54-45=9. then the answer is 63.

There are two possible ways to get to the answer.

OPTION 1: We have two numbers, $a=\overline { xy } =10x+y$ and its reversed number $b=\overline { yx } =10y+x$ . We know that the digit sum of $a$ (that will be the same as $b$ , because they have the same digits) is $x+y=9$ . Solving the system of equations $\begin{cases} x+y=9 \\ a-b=27 \end{cases}\rightarrow \begin{cases} x+y=9 \\ 10x+y-10y-x=27 \end{cases}$ ,

We'll get:

$\begin{cases} x+y=9 \\ 9x-9y=27 \end{cases}\rightarrow \begin{cases} x+y=9 \\ x-y=3 \end{cases}\rightarrow \begin{cases} x+y=9 \\ x-y=3 \end{cases}\rightarrow$ $y=9-x\rightarrow x-(9-x)=3\rightarrow 2x=12\rightarrow \boxed { x=6 } \rightarrow \boxed { y=3 }$ . So, the solution is $\boxed{a=63}$ ; and its reversed number is b=36.

OPTION 2: As the digit sum of the number is 9, this number has to be a multiple of 9, let's call it $a=9 \times n$ . Since the number we'll get when we reverse the number will have the same digits, it will have the same digit sum, so it will also be multiple of 9. Let's call this number $b=9 \times m$ . Since $27=9 \times 3$ , we will have $a-b=27$ , $9 \times n-9 \times m=9 \times 3$ ,. So, we have $n-m=3$ . The only 2-digit multiple of 9 that satisfies this is 63, as $63=9 \times 7$ and its reversed number is 36 $36=9 \times 4=9 \times (7-3)$ .

OMG I'm in the 63% who solved this and the answer is 63? Coincidence? I think not.

If you list all the possible combinations it would be 81,72,63, and 54. 81-18 is obviously going to be over 27, 72- 27 is 45 so that one is marked out. 54-45 is going to be way to small. So it has to be 63 just to check, 63-36=27. So 63 is your answer.

Two digit number is written as 10x+y and its reverse is written as 10y+x now the diff of these two is 9(x-y) so, 9(x-y) = 27 therefore x-y = 3

and also given x+y = 9 solving the last two equations we get x=6 and y=3

let the no. be 10x+(9-x)

Then

10x+(9-x) = 10(9-x)+x + 27

10x+9-x = 90-10x+x+27

18x = 108

x = 6

9-x = 3

therefore the no is 63