Let the tens and units digits of the required number be x and y respectively. Then,
`xy=18impliesy=(18)/(x)" "…(i)`
And, `(10x+y)-63=10y+x`
`implies" "9x-9y=63impliesx-y=7" "…(ii)`
Putting `y=(18)/(x)` from (i) into (ii), we get
`x-(18)/(x)=7`
`impliesx^(2)-18=7ximpliesx^(2)-7x-18=0`
`impliesx^(2)-9x+2x-18=0impliesx(x-9)+2(x-9)=0`
`implies(x-9)(x+2)=0impliesx-9=0" or "x+2=0`
`impliesx=9" or "x=-2`
`impliesx=9" "[because" a digit cannot be negative"].`
Putting x=9 in (i), we get y=2.
Thus, the tens digit is 9 and the units digit is 2.
Hence, the required number is 92.
