Hello from MrBillDoesMath!
Answer:
58
Discussion:
Suppose the 2-digit number is "ab". That is, 10a + b.
Sum of digits = 13 => a + b = 13 (*)
Digits reversed if 27 added to number => (10a + b) + 27 = 10b + a (**)
(**) =
(10a + b) + 27 = 10b + a => subtract 10b, then a, from both sides
9a -9b = -27 => divide both sides by 9
a - b = -3
From (*), a+ b = 13 so
(a-b) + ( a+b) = -3 + 13 =>
2a = 10 =>
a = 5
As a +b = 13, 5 + b = 13 => b = 8
Hence the number "ab" is 58
Thank you,
MrB