Question

A two-digit number is such that the product of its digits is 18.If 63 is subtracted from the number,the digits interchange their places.Find the number.

Answer 1

let the two digit number be 10x+ y

ATQ,.
x × y= 18..........(1)
and
10x + y - 63 = 10 y + x
9x - 9y - 63= 0
9x - 9y = 63
x-y = 7..........(.2)
x= 7+y
put value of x in eq 1b, we get
( 7+y ). y = 18
y² + 7y = 18
y² +7y-18=0
y² +9y -2y -18= 0
y(y+9) -2 ( y +9) =0
( y+9) (y-2). = 0
y=-9 , y = 2
y= 2
so, x= 7+2=9

therefore the two digit number is 10(9)+2=92

answer = 92