Let 'n' be the original number
Let 'a' be the digit in the ten's place of 'n'
Let 'b' be the digit in the one's place of 'n'
Then, n = 10a + b
We have,
a+b = 11 -------- (equation 1)
Let m be the number formed when the digits of n are reversed
Then, m = 10b + a
Given that, m = n + 27
=> 10b + a = (10a + b) + 27
=> 9b - 9a = 27
=> 9(b - a) = 27
=> b - a = 3 ----- (equation 2)
Adding equation 1 and 2, we get
2b = 14
=> b = 7
putting b = 7 in equation 1
a + 7 = 11
=> a = 4
Therefore original number is 10×4 + 7 i.e. 47
