Question

A two digit number is such that product of its digit is 18 When 63 is subtracted from the number the digit interchanged their place Find the number

• A. $92$
• B. $56$
• C. $88$
• D. $71$

Answer 1

The correct option is A $92$

Let the number be $10x+y$
According to question,
$10x+y-63=10y+x$
$\Rightarrow 10x-x+y-10y=63$
$\Rightarrow 9x-9y=63$
$\Rightarrow x-y=7$
$\Rightarrow x=7+y$ (i)
$xy=18$ (ii)
Substituting the value of $x$ in (ii) we get,
$(7+y)y=18$
$\Rightarrow y^2+7y-18=0$
$\Rightarrow y^2+9y-2y-18=0$
$\Rightarrow y(y+9)-2(y+9)=0$
$\Rightarrow (y+9)(y-2)=0$
$\Rightarrow y=-9$ and $y=2$
$y=-9$ is not valid
$\therefore y=2$
Putting the value of $y$ in (i) we get,
$x-2=7$
$\Rightarrow x=7+2$
$\Rightarrow x=9$

So the number $=10x+y=10\left(9\right)+2=92$