Question

The sum of the digit of a two digit number is 9. number formed by interchanging the digit is 45 more than the original number.find the original number and check the solution

Answer 1

Let's the two digits be x and y
According to the question
x+y=9
so, x=9-y
and,Without changing the place
(10)x+y=10x+y
putting the value of x
10(9-y)+y
=90-10y+y
=90-9y
Interchanging the place
10y+x
=10y+9-y
=9y+9
according to the question
90-9y=9y+9+45
90-9y=9y+54
90-54=9y+9y
36=18y
y=36÷18
y=2
so,x=9-y=9-2=7
The two digit number is 72
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Answer 2

Answer:

Let the tens digit of the number be x.

And the unit digit be y.

Two digit number = 10x + y

Number formed by interchanging the digits = 10y + x

According to condition,

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

According to second condition,

10y + x = 10x + y + 45

$⟶$ 10y + x - 10x - y = 45

$⟶$ 9y - 9x = 45

$⟶$ y - x = 5 - - - ( Diving by 9 ) - ( 2 )

Now,

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

- x + y = 5 - - - ( 2 )

_____________

$⟶$ 2y = 14 ( Adding both equations )

$⟶$ y = 14 / 2

$⟶$ y = 7

Put y = 7 in equation ( 1 ),

$⟶$ x + y = 9

$⟶$ x + 7 = 9

$⟶$ x = 9 - 7

$⟶$ x = 2

The original number = 10x + y

$⟶$ 10 × 2 + 7

$⟶$ 20 + 7

$⟶$ 27

The original number is 27.