Question

A two digit number is such that the product of its digits is 12. When 9 is added to the number, the digits inter change their places. Determine the number

Answer 1

Let the ten's digit and the one's digit be x and y respectively.

Given

Product of the digits = 12

$\implies xy = 12$

When 9 is added to the number, the digits inter change their places.

$\implies 10x+y+9=10y+x$

$\implies 10x-x+y-10y = -9$

$\implies 9x-9y = -9$

$\implies x-y=-1$

$\implies -y=-1-x$

$\implies y = x+1$

Substituting y in the first equation, we get,

$x(x+1)=12$

$\implies x^{2} +x-12=0$

$\implies x^{2} -3x+4x-12=0$

$\implies x(x-3)+4(x-3)=0$

$\implies (x+4)(x-3) = 0$

Now,

$x+4=0\\\implies x = -4$

Negative values are not acceptable

Therefore  

x = 3

=> y = 3 + 1 = 4

$\boxed{\boxed{\bold{Therefore, \ the \ required \ number \ is \ 34}}}}}$

                                                                           

Answer 2

Answer:

The number is 34

Step-by-step explanation:

Let the tens digit number be x

Let the ones digit number be y

Therefore,

The number is 10x + y

Product of the digits = xy

=> xy = 12. ------------- ( 1 )

When 9 is added to the number, the digits interchange their places. So,

10x + y + 9 = 10y + x

=> 9y - 9x = 9

=> y - x = 1

=> y = x + 1

Putting above value of y in ( 1 ), we get

=>( x ) ( x + 1 ) = 12

=> x² + x - 12 = 0

=> x² + 4x - 3x - 12 = 0

=> ( x + 4 ) ( x - 3 ) = 0

=> x = -4 or x = 3

Since, the product is positive, digits cannot be negative.

Therefore,

x = 3

So, y = 4

ANSWER) The number is 34.

Thanks !!