Question

Find PLZZ
.......
.......

Answer 1

Let the unit digit be x
Let the tenth digit be y
x + y =12
10x + y  -  10y -x=18 
9x - 9y =18
x - y =2
solving the equations 
x=7
y=5
number =10 x + y
             = 57

Answer 2

Solution:

_____________________________________________________________

Given:

Statement 1 : The sum of digits of a two digit number is 12.

Let the tens digit of the number be x,
Let the ones digit of the number be y,

=> x + y = 12,. ..(i)

&

So, the value of the number = 10x + y,.

_______________________________

Statement 2: The number obtained by interchanging the digit exceeds the given number by 18,.

The original number = x y = 10x + y,

The number obtained by interchanging the digits = y x = 10y +x,.

=> 10x + y + 18 = 10y + x

=> 10x -x + y - 10y + 18 = 0

=> 9x - 9y = -18

=> x - y = -2...(ii)

_____________________________________________________________

To find :

The original number (10x + y)

_____________________________________________________________

Adding equations (i) & (ii),

We get,

=> (x + y) + (x - y) = 12 + (-2)

=> 2x = 10

=> ∴ x = 5,.
_________

Substituting value of x in equation (ii),

we get,

=> x - y = -2

=> 5 - y = -2

=> -y = -2 - 5

=> ∴ y = 7...

The original two digit number is,

=> 10x + y

=> 10(5) + 1(7)

=> 50 + 7

=> 57,.

_____________________________________________________________

                                         Hope it Helps !!