Question 570234
Let
x and y are two digits of a number
number = n



Sum of the digits 
x+y=6.....................(1)
When x is ten and y is unit
10x+y=n.............(2)
When the digits are reversed, the new number is 36 more than the original number
Now y is ten and x is unit
10y+x=n+36.............(3)
Subtract (2) from (3)
10y+x=n+36.............(3)
-10x-y=-n.............(2)
-------------------------
-9x+9y=36
9(y-x)=36
9(y-x)/9=36/9
y-x=4...................(4)
Add (1) and (4)
y-x=4...................(4)
x+y=6.....................(1)
-----------------------------
2y=10
2y/2=10/2
y=5
Put the value of y in (1)
x+5=6.....................(1)
x=6-5
x=1

Number =  15
When the digits are reversed = 51 (15+36=51)