the sum of a two digits of a two-digit number is 10. when the digits are reversed, the new number is 36 more than the original number. find the original number.

Answer 1

let the unit digit be x and the tens digit be y
so the number is 10y + x

if we reverse the digits, the number is 10x + y

10x + y - (10y + x) = 36
9x - 9y = 36
x - y = 4
but we also know that x + y = 10
add them
2x = 14
x = 7, then y = 3

the original number was 73

check:
73-37 = 36 , all is good