Question

the sum of digits of a two digit number is 9 if the number formed by reversing the digit is less than original number by 9 find the original number

Answer 1

Hey friend your answer is here
$let \: tens \: digit \: be \: x \: \\ and \: unit \: digit \: be \: y \\ the \: number \: = 10x + y \\ x + y =9 \\ x = 9 - y \\ according \: to \: question \\ 10x + y - 9 = 10y + x \\ 10x + y - 10y - x = 9 \\ 9x - 9y = 9 \\ 9(x - y) = 9 \\ x - y = 1 \: \: \: \: .... i\\ putting \: the \: value \: of \: x \: in \: equation \: no. \: (i) \\ 9 - y - y = 1 \\ - 2y = 1 - 9 \\ - 2y = - 8 \\ y = 4 \\ x = 9 - y \\ 9 - 4 \\ = 5 \\ the \: no. = 10x + y \\ = 10(5) + 4 \\ 54$