Answer:
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.
