Question

Sum of two digits of a two digit number
is 9 when We interchange the digits,
it is
found that the nesulting number is greter
than the original no by 27 What is the two
digit number?
​

Answer 1

Answer:

$\sf{Let \: the \: digits \: be \: x \: and \: y.}$

$\sf{Then, \: x+y = 9}$

$\sf{The \: original \: number \: is \: 10x+y.}$

$\sf{On \: reversing, we \: get \: the \: new \: number \: as \: 10y+x}$

$\sf{The \: new \: number \: is \: greater \: than \: the \: old \: number \: by \: 27, i.e.}$

$\sf(10y+x) - (10x+y) = 27$

$\sf{or \:9y-9x = 27, or\: y-x = 3}$

$\sf{and \: x+y = 9}$

$\sf{Adding \: the \: two \: equations, }\\ \sf{ \: we \: get \: 2y = 12 \: or \: y = 6.}$

$\sf{Thus, x = 3.}$

$\bf{Therefore, \: the \: original \: number \: is \: 36.}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━