Let the digits of the number we need to find be ab. So the number is 10*a + b. The digits are reversed when 27 is added to it.

We can use this to create the equation: 10*a + b + 27 = a + 10*b

=> 9*a - 9*b = -27

=> b - a = 3

So we have b as 1, 2, 3, 4, 5 or 6 and a is 4, 5, 6, 7, 8 or 9

Therefore for all the numbers 14 , 25 , 36 , 47 , 58 and 69 the digits are reversed when 27 is added.

**The required numbers are 14 , 25 , 36 , 47 , 58 and 69**