Question

a number consist of two digit number whose sum is 9 if 27 is added to the number the digit are reversal.find the number

Answer 1

$Heya \: !!! \\ \\ This \: is \: your \: answer. \\ \\ It \: is \: given \: that \: the \: sum \\ \: of \: the \: two \: digits \: is \: 9. \\ Let \: the \: digit \: at \: tens \: place \: be \: b \: \\ and \: ones \: place \: be \: a. \: \\ \\ So.... a + b = 9. .......(i).$
$If\: 27 \: is \: added \: to \: the \: original \: number, \\ the \: digits \: get \: reversed. \\ eg. \: if \: the \: original \: number \: is \: AB, \\ then \: after \: adding \: 27 \: it \: becomes \: BA. \\ \\ We \: know \: that \: every \: number \: is \: of \: \\ the \: form ....... \\ ..... + ..... + 1000d + 100c + 10b + a.$


$As \: it \: is \: a \: two \: digit \: number, \: then \: \\ it's \: general \: form \: will \: be. \: \\ 10b + a$
$So..... \\ According \: to \: question, \\ 10b+a +27 = 10a+ b \\ 10b - b + a - 10a = - 27 \\ 9b - 9a = - 27 \\ b - a = - 3 \\ a - b = 3..........(ii)$

$Now, \: adding \: equation \: (i) \: and \: (ii), \\ we \: get... \\ \: \: \: a \: \: + \: \: b \: = \: 9 \\ \: \: \: a \: \: - \: \: b \: = \: 3 \\ ........................ \\ \: \: 2a \: \: \: \: \: \: \: \: \: \: \: = \: 12$

$Hence, \: a = 6. \\ Putting, \\ a = 6 \: in \: equation \: (i), \\ a + b = 9 \\ 6 + b = 9 \\ b = 3.$
$Now, \: a = 6 \: and \: b = 3. \\ \\ Putting \: this \: in \: the \: general \\ form \: of \: original \: number,$
$10b + a \\ = 10 \times 3 + 6 \\ = 36.$


$Hence, \: the \: original \: digit \: is \: 36.$
$Hope \: it \: helps. \\ Regards.........$

Answer 2

Answer:

36

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