Question

number in is such that the product of the digits is 18 when 63 is subtracted from the number the digits interchange their places find the number

Answer 1

Product =18
Interchange the no. =63

No. 3,6
3×6 =18
36 interchange 63

Answer 2

Let the unit digit be x and tens digit be y.

Given,

x*y = 18

y=18/x

Number = 10y+x

Number after interchanging = 10x+y

10y+x-63=10x+y

-9x+9y=63

-9(x-y)=63

x-y= -7

x-18/x= -7

x^2-18= -7x

x^2+7x-18=0

x^2+9x-2x-18=0

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

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

x=2       (Since digit can't be negative)

x=18/y = 2=18/y

y=9

Number = 10y+x = 92