Question

The sum of the digits 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 .


Step by step explanation please. ​

Answer 1

Answer: The original number is 27.

Step-by-step explanation:

The sum of the digits =2+7 =9

If the digits interchanged we get 72.

72-27 =45.

I hope it is helpful.

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.