Question

The sum of the digits of a 2 digit number is 9.The number formed by interchanging the digits is 45 more than the original number. Find the original number.

Answer 1

let the two digit is x and y

then, the number is = 10x+ y

x+y=9... (i)

and 1Oy+x=10x+y+45

9y-9x=45...(ii)

Now (i)×9+(ii)×1,

9x+9y=81

9y-9x=45

........................

18y=126

y=126/18

: .y=7

then,x=9-7=2.

so the number is = 10×2+1×7

=20+7=27

Ans:27

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.