When you reverse the digits in a certain two-door number you increase its value by 27. what is the number if the sum of its digits is 11?

Ab has a value in the decimal system as:

10a+b

This number reversed has a value of 10b+a and we are told that this value is 27 more than the original so

10b+a+27=10a+b

9b-9a+27=0  

9b-9a=-27

b-a=-3  

a=b+3  and we are also told that a+b=11, b=11-a so

a=11-a+3

2a=14

a=7 and b=4

So the original number was 47

check...

74-47=27

and 

7+4=11