Question

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number?​

Answer 1

Answer:

let the number be xy.

x+y=9 ( 1 )

yx>xy

yx=xy+27

10y+x=10x+y+27

10y+x-10x-y=27 (after transposition)

9y-9x=27

9(y-x)=27

y-x=3  ( after shifting 9 to the RHS it will be divided and the answer obtained would be 3)

y-x=3

x+y=9

x and x will get cut because they have opposite signs.

2y=12

y=6

So, if we bring statement ( 1 ) back in mind, it would mean:

x+y=9

x+6=9

x=3

The numbers are 36 and 63.

PLEASE MARK AS BRAINLIEST.

Step-by-step explanation:

Answer 2

Answer:

63 is the 2 digit number. Please mark this answer as brainliest. Happy Tuesday!

Step-by-step explanation:

let one digit be "x" and the other digit be "y"

x + y = 9 -----------------Equation 1

Also, when you reverse digits the difference is 27. Let's put this in an equation -    

   (10x + y) - (10y + x) = 27

⇒ 10x + y - 10y - x = 27

⇒ 9x - 9y = 27

⇒ 9 (x - y) = 27

⇒ x - y = 3 -----------------Equation 2

Now, the derive value of y from Equation 1 -  

   x + y = 9

⇒ y = 9 - x-----------------Equation 3

Lets substitute the above value of Y in Equation 2.

   x - y = 3

⇒ x - (9 - x) = 3

⇒ x - 9 + x = 3

⇒ 2x = 12

⇒ x = 12/2 = 6

Now apply this value of x in Equation 1.

   x + y = 9

⇒ 6 + y = 9

⇒ y = 3

Hence the two digit number is 63.