Question

A two digit number is such that the product of its digits is 8. If 18 is subtracted from the number the digits interchangetheir places

Answer 1

Let the digit at tens place be x and at units place be y
hence number is 10x+y
Now product is 8

Hence

xy=8


By second condition
10x+y-18=10y+x
$9 x - 9y = 18 \\ x - y = 2$
x=y+2
put in 1
$xy = 8 \\( y + 2)y = 8 \\ {y }^{2} + 2y = 8 \\ {y}^{2} + 2y - 8 = 0 \\ (y + 4)(y - 2) = 0$
Hence
y=-4 or y=2

But digit can not be negative
so y=2

Put in 1
x=4

Hence number is
$10x + y \\ = 10 \times 4 + 2 \\ = 42$