Question

Sum of the digits of a two digits number be 9 . when we interchange the digits it's found that the resulting new number is greater than original number by 27. what is the two - digits number ??​

Answer 1

Let digit at tens place be X

'' digit at ones place be Y.

Original number = 10X + Y

New number = 10Y + X

Given:

X + Y = 9... eq.(I)

New number = Original number + 27

=> 10Y + 10X = 10X + Y + 27

=> 9y - 9x = 27

=> Y - X = 3 => -X + Y = 3... eq(ii)

On solving eq(i) and eq(ii), we get:

X = 3, Y = 6

Therefore, original number = 36

New number = 63

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 109–x + x

Let us reverse the digit

the number becomes 10x + 9–x

As per the given condition

10x + 9–x = 109–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