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

Original number = 36

Step-by-step explanation:

Let unit place digit is = x

and ten's place digit = y

so original Number = 10y + x

According to question,

Case (1st) sum of digit = 9

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

=> y = 9 - x

Now when we reverse the digit,

unit place digit is = y

and ten's place digit = x

Reverse or new  number = 10x + y

According to question,

Case (2nd) resulting new number is greater than the original number by 27

$=> 10x + y = 10y + x +27\\=> 10x + y -10y - x = 27\\=> 9x - 9y = 27\\=> 9(x -y) = 27\\=> x- y = 27/9\\=> x -y = 3$

Now from equation 1 putting y = 9 - x

$=> x - (9-x) =3$

$=> x - 9 + x = 3\\=> 2x = 3 + 9\\=> 2x = 12\\=> x = 12/2 = 6$

Now As,  $y = 9 -x$

$=> y = 9 - 6 = 3$

So As original number = 10y + x

=> original number = 10(3)  + 6

=> original number = 30 + 6

=> original number = 36

Answer 2

Answer:

$\huge\green{\boxed{\sf Answer}}$

Given

The sum of the two digits = 9

On interchanging the digits, the resulting new number is greater than the original number by 27.

Let us assume the digit of units place = x

Then the digit of tens place will be = (9 – x)

Thus the two-digit number is 10(9 – x) + x

Let us reverse the digit

the number becomes 10x + (9 – x)

As per the given condition

10x + (9 – x) = 10(9 – x) + x + 27

⇒ 9x + 9 = 90 – 10x + x + 27

⇒ 9x + 9 = 117 – 9x

On rearranging the terms we get,

⇒ 18x = 108

⇒ x = 6

So the digit in units place = 6

Digit in tens place is

⇒ 9 – x

⇒ 9 – 6

⇒ 3

Hence the number is 36