Question

A two digit number is such that the product of its digit is 20. If 9 is added to the number, the digits interchannge their place. Find the number

Answer 1

$\huge\boxed{\fcolorbox{blue}{orange}{HELLO\:MATE}}$

Let us take the digital at ones place be x and at tens place be y.

So,

$\large\green{\boxed{Original\: number = 10y+x}}$

Now,

Product of its digit =y×x=xy.

ATQ, xy=20.

so y =20/x ......... 1

$\large\green{\boxed{Reversed\: number = 10x+y}}$

Atq, 10y+x+9=10x+y

or 10x-x+y-10y=9

or 9x-9y=9

or9(x-y) =9

So, x -y =1. ............. 2

or x - 20/x = 1 (from....... 1)

or x^2-20/x=1

or x^2-20=x

or x^2-x-20=0

or x^2-5x+4x-20=0

or x(x-5) +4(x-5) =0

or(x+4) (x-5) =0

or x+4=0 | or x-5 =0

Therefore x =-4or5

Since the unit digit can't be negative

So x =5

Now from.... 2

x - y =1

or 5-y=1

Therefore y =4

so,

$\large\purple{\boxed{Required \:no. =10x+y = 45}}$