2-digit number is 18
Step-by-step explanation:
Let x= ten's digit and
y= one's digit
The sum of two digits is 9
so, x+y = 9
When you reverse its digits you increase the number by 63.
10y+x=10x+y+63
10y-y+x-10x=63
9y-9x=63
So, we have two equations:

Solving these equations to find value of x and y:
Let:

Multiply eq(1) by 9 and add both equations:

So, value of y=8
Now, finding value of x:
Putting value of y in eq(1)

So, value of x=1
The value of x is 1 and value of y = 8
So, 2-digit number is 18
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