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 digits be x(tens) and y(units)

x+y = 9, so x = 9 - y

10y+x = 10x+y + 27

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

10y +9 - y = 90 -10y + y + 27

9y + 9 =117 -9y

18y = 117-9

y = 108/18

Therefore, y=6

x+y=9 So, x=3

Therefore, x=3, y=6

Hope this helps.

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