Spicy number

Let the number be $10x+y$ and its digits be $x$ and $y$ .

$(x*y)+(x+y)=10x+y$

$\Rightarrow$ $xy+x+y=10x+y$

$\Rightarrow$ $xy-9x=0$

$\Rightarrow$ $x(y-9)=0$

$\Rightarrow$ $x=0$ or $y=9$

Since , $x=0$ gives a 1-digit number,so $y=9$ and $x$ can any values between $1$ and $9$ .

Second largest spicy number is $\boxed{89}$ .

if digits are x, and y and the number is 2digits, then the number is 10x + y so the equation is: 10x + y= x + y + xy y is on both sides so we can cancel y off resulting in: 10x= x+ xy 10x= x(1 +y) 10= y+1 y= 9 x= any number from 1-9 So largest spicy number=99 Second= 89