When you reverse the digits in a certain two-diget number you increase it value by 27. What is the number if the sum of its digits is 5

14 or 41

41 - 14 = 37

4+1 = 5

The number is = 10x+y

if reverse the digits, the number is: 10y+x

The sum fo its digits is = x+y=5

I suggest this system of equations:

(10y+x) - (10x+y) = 27 ⇒9y-9x=27

x+y=5

We can solve this system of equations by equaliztion method

x=5-y

9y-9 (5-y) = 27

9y-45+9y=27

18y=27+45

18y=72

y=72/18

y=4

x=5-y

x=5-4=1

The number is: 10x+y=10 (1) + 4=14

Answer: the number is 14