Question 279490
.
The sum of the digits of a two- digit number is 12. If 36 is added to the number, then the number obtained 
is the original with its digits interchanged. Find the original number.
~~~~~~~~~~~~~~~~~~~~~~~~~



        The solution in the post by @mananth, giving the answer '43 ' is incorrect,

        as anybody can check by substituting it to the problem.


        I came to bring a correct and accurate solution.



Let x be in the tens place and y in units place
x+y =12
10x+y+36 = 10y+x
10x-10y+y-x+36=0
9x-9y=-36
x+y=12
9x+9y=108
18x=72
x=4
x+y=12 but x=4 so y=8. 


The number is 48.   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>


Solved correctly.