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
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Answer 1

Let’s say x is the unit digit and y is the tenth digit.

y+x = 9 -> y=9-x

10x+y = 10y+x+27

10x+9-x = 10(9-x)+x+27

10x+9-x = 90–10x+x+27

18x = 108

x = 6

so y = 3

let’s check

63 - 39 =27

27 = 27 (correct)

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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.