Sum of the digits of a two digit number is 9

Explanation:

Let the digit at ten’s place be x.

The digit at one’s place be 9 – x

Therefore the original number is 10x + 9 – x = 9x + 9

If the digits are interchanged;

The digit at one’s place be x.

The digit at ten’s place be 9 – x

Therefore, the new number is 10(9 – x) + x = 90 – 10x + x

= 90 – 9x

According to the given question;

New number = Original number + 27

The digit at ten’s place is 3

The digit at one’s place is 9 – 3 = 6

Therefore, the two digit number is 36 respectively.

Final answer:

Hence, the two digit number is 36.