Question 519069


let xy be the number, where x is the first digit and y the second one.
  
 based on the question, x+y=x*y/2 and x*y=yx/2  ( yx represents a number not a product)

so we have,  x+y=x*y/2
             x*y= (10y+x)/2    

             2(x + y)= x*y
             x*y= (10y+x)/2
 
 so, 2(x+y)=(10y+x)/2    
    2*2(x+y)=2(10y+x)/2
      4(x+y)=10y+x
      3x=6y
      x=2y
 we know that x and y are integer numbers because they are digits of a number. 
   
 the question says, one of the digit is 6 but we let's say y is the one who is 6
 if y=6, we would have, x=2*6=12, and this  would  make any sense since x is supposed to be a digit not a number, so y is not 6. since y is not 6,  we can affirm the digit that is 6 is x.

 so x=6 ,    y=x/2=6/2=3.

so  xy=63. 

the answer is 63.

we can check our answer.
6+3=(6*3)/2 and 6*3=36/2