Question

The difference of the digit of a two digit number is 3 if the digits are interchanged and the new number is added to the original number the result is 77

Answer 1

let the original number be xy in which ten's place digit is x and unit's place digit is y so it can be expressed as 10x+y. When interchanged , y is replaced by x in the unit's place and their difference is 3 => y-x=3 or x-y=3 . And when reversed number is added to original number, the result is 77=> 10x+y+10y+x=77=> 11x+11y=77=> x+y =7 . So let's add x+y=7 and x-y=3 => 2x=10=> x=5 and y=2 . So number is 52 in first case .In second case let's add
x+y=7 and y-x=3 => 2y=10=> y=5 and x=2 .The number in this case is 25. So the number can be 25 or 52.