Question

The sum of two digit number is 8 . The digit are interchanged when 18 is substracted from it what is the number ? explain.

Answer 1

$let \: the \: number \: be \: 10x + y \\ here \: x + y \: = 8..(1) \\ \\ reversing \\ (10x + y) \: - (10y + x) = 18 \: ..(2) \\ equation \: 2 \: becomes \: \\ 10x + y \: - 10y - x \: = 18 \\ 9x - 9y = 18 \\ x - y = 2..(3) \\ x + y = 8 ..(1) \\ add \: (1) \: and \: (3) \: to \: get \: \\ 2x = 10 \: x = 5 \: \\ then \: y = 8 - 5 = 3 \\ \\ hence \: the \: number \: 10*5+3 =53\: and \: reverse \: is \: 35$