Question

a number consist of two digits whose product is 18. When 27 is subtracted from the number , the digits change their places. find the number.

Answer 1

Let us assume the number is xy
i)As per the equation x×y=18......................................1)
The number = 10x+y
The number with digits interchanged 10y+x
therefore 10x+y -27=10y+x
9(x-y)=27
x-y=3.............................................................................2)
(x+y)²-(x-y)²=4xy
x+y=√(x-y)²+4xy
√(9+4×18)=√81=9
so x+y=9.........................................................................3)
adding eq 2&3 we get 
2x=12
so x=6
substitute x value in eq 3 we get y=3
hence the required number is 63.