Question

a two digit number is such that the product of its digits is 18.when 63 is subtracted from the number,the digits interchange their places.find the number.

Answer 1

I think the number is 36

Answer 2

Let the number at ten's place be x
& at one's place be y

then according to first case,

Product of digit is 18

x y=18........i

Now Second case:-

Original number is 10x+y

(10x+y)-63=10y+x

10x-x+y-10y=63

9x-9y=63

x-y=7

x=7+y.......ii

=>Putting value of x from ii equation in i equation,
we get

x y=18

(7+y)y=18

7y+y²=18

y²+7y-18=0

=>Now, by middle term splitting

y²+7y-18=0

y²+9y-2y-18=0

y(y+9)-2(y+9)=0

(y+9)(y-2)=0

(y+9)=0
y=-9

(y-2)=0
y=2

⭐If y = -9

then x=7+y
x=7+(-9)
x=-2

Then the number will be

10x+y

= 10×(-2)-9

= -20-9

= -29

⭐If we take y=2
Then, x=7+y

x=7+2

x=9

Then the number will be

10x+y

= 10×9+2

= 90+2

= 92

Now,

The number can be -29 & 92


@Altaf