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 :-

• The number is 36.

Given :-

• 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

To Find :-

• The two digit number.

Solution :-

Let

• Digit at ten's place be x
• Digit at one's place will be 9 - x

Original number :-

⇒ 10x + (9 - x)

⇒ 10x + 9 - x

⇒ 9x + 9

New number :-

⇒ 10(90 - x) + x

⇒ 90 - 10x + x

⇒ 90 - 9x

→ It is given that the resulting new number is greater than the original number by 27.

According to question :-

⇒ 90 - 9x = 9x + 9 + 27

⇒ 90 - 9x = 9x + 36

⇒ 90 - 36 = 9x + 9x

⇒ 54 = 18x

⇒ x = 54/18

⇒ x = 3

Now

• Ten's place digit = x = 3
• One's place digit = 9 - x = 9 - 3 = 6

→ Number = 36

Hence, the number is 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