GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Let one's digit is y and ten's digit is $\mathit{x}$ Hence the number becomes '10x +y' and the reverse number will be ' $10\mathit{y}+\mathit{x}$ '
$\mathit{x}+\mathit{y}=9$ . . .(i)
$10\mathit{x}+\mathit{y}-10\mathit{y}-\mathit{x}=45$
$\mathit{x}-\mathit{y}=5$.....(ii)
Adding (i) and (ii)
$\mathit{x}=7$
Subtracting (i) and (ii)
$\mathit{y}=2$
Therefore the number is 72 .