Question

the sum of the digit of the two digit number is 9 if 9 is added to the number the digits interchange their places find the number​

Answer 1

Answer:

Here is your answer

Step-by-step explanation:

Let tens digit be x

Let ones digit be y

=> Number- 10x+y

     Number with interchanged digits- 10y+x

x+y=9 (Given) --------------(1)

10x+y+9=10y+x (Given)

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

9x-9y=-9

9(x-y)=-9

x-y=-1 ---------------------------(2)

(1)+(2)=> 2x=8

x=4

y=5

∴Number is 10x+y

               =10X4+5

                =45

Answer 2

Answer:

The original two digit number is 45.

Step-by-step-explanation:

Let the digit at the tens place be x.

And the digit at the units place be y.

Two digit number = xy

$\implies\:$ Two digit number = 10x + y

Also,

The number obtained by interchanging the digits = yx

$\implies\:$ The number obtained by interchanging the digits = 10y + x

From the first condition,

x + y = 9 - - - ( 1 )

From the second condition,

The original number + 9 = Number obtained by interchanging the digits

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

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

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

$\implies\:$ x - y = - 1 - - - [ Dividing both sides by 9 ] - - ( 2 )

Adding both equations, we get,

x + y = 9 - - - ( 1 )

+ x - y = - 1 - - - ( 2 )

______________

$\implies\:$ 2x = 8

$\implies\:$ x = 8 / 2

$\implies\boxed{\red{\sf\:x\:=\:4}}$

By substituting x = 4 in equation ( 1 ), we get,

$\implies\:$ x + y = 9

$\implies\:$ 4 + y = 9

$\implies\:$ y = 9 - 4

$\implies\boxed{\red{\sf\:x\:=\:5}}$

Two digit number = 10x + y

$\implies\:$ 10 × 4 + 5

$\implies\:$ 40 + 5

$\implies\:$ 45

The original two digit number is 45.