Question

The product of the digits of a two-digit number is twice as large as the sum of its digits. If we subtract $27$ from the required number, we get a number consisting of the same digits written in the reverse order. Find the number.

Answer 1

Let the two digit number be $10x+y$

Given conditions, $xy=2(x+y)$(equation $1$)

$10x+y-27=10y+x$

$\Rightarrow x-y=3$

$\Rightarrow y+3=x$ (equation $2$)

Substituting $2$ in $1$,

$y^2-y-6=0$

$\Rightarrow (y-3)(y+2)=0$

$y=3,y=-2$

If $y=3$, then $x=6$

The given number is $63$