The sum of the digits of a two-digit number is equal to 15. If these digits switch places then you will get a number that is 27 less than the original number. What is the original number and reversed number?

Let n and m be single digit numbers. The information in the question can be translated into

Original number:

10n + m,

where

n + m = 15

New number:

10m + n = (10n + m) - 27 ⇒ 9n - 9m = 27 ⇒ n - m = 3

Solve for n and m in

n + m = 15

n - m = 3

and get

2n = 18

n = 9

m = 15 - n = 15 - 9 = 6

n = 9

m = 6

Test the answer.

n + m = 9 + 6 = 15

The original number is 96.

96 - 27 = 69, which is 96 with reversed digits

The new number is 69.