Question

Sum of the digits of a two digit number is 11. the given number is less than the number obtained by interchanging the digits by 9 . find the number (liner equation in one variable)

Answer 1

Answer:

$The \: number \: is \: 65.$

Mark Brainliest if seems appropriate!

Step-by-step explanation:

$Let \: the \: two \: digits \: be x \: and \: y, \: where \: x \: is \: in \: Ten's \: place \: and \: y \: is \: in \: Unit \: place. \\ </p><p>Therefore \: the \: two \: digit \: number \: is \: (10x + y). \\ number \: obtained \: by \: interchanging \: the \: digits \: is \: (10y + x). \\ By \: given \: conditions, \\ (x + y) = 11 ..............................(i) \\ (10x + y) - 9 = (10y + x)..............................(ii) \\ Therefore \\ 10x + y - 9 = 10y + x \\ 9x - 9y = 9 \\ x - y = 1..............................(iii) \\ Adding \: equation \: (i) \: and \: (iii) \: we \: get \: (x + y) + (x - y) = (11) + (1) \\ 2x = 12 \\ x = 6. \\ Therefore \: x + y = 11 \\ 6 + y = 11 \\ y = 5. \\ Now \: (10x + y) = (10)(6) + 5 = 65 \\ </p><p>Therefore \: the \: number \: is \: 65.</p><p></p><p>$