A number of two digits, written "ab" has value  10a + b



4(a+b) = 10a + b              (eq 1)



Reversing the digits means writing it as "ba" which has value 10b + a:



10b + a = (10a + b) + 27      (eq 2)



Simplify both equations:

(eq 1) simplifies to  2a - b = 0  ---> b = 2a

(eq 2) simplifies to   b - a = 3  

Using substitution (b = 2a) into the simplified (eq 2)  gives

      2a - a = 3     or    a = 3   --->  b = 6

The number is 



Check:

4(3+6) = 4*9 = 36  (ok on first condition)

63 = 27 + 36    (ok on 2nd condition)

 

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