Reversing the digits in john's age results in his father's age. the positive difference between their ages is 27 years. if the sum of the digits in each age is 5, what is the number of years in john's father's age?

When you reverse the digits of a 2-digit number, the value changes by 9 times the difference in the values of the digits. The problem statement is telling you the difference of the two digits is 27/9 = 3 and the sum of the two digits is 5. Then the digits must be 4 and 1.

John's father is 41.


John is 14.

___
This is two problems in one, a "reversed digits" problem and a "sum and difference" problem.

If you have digits x and y, when x is the 10s digit, the value is (10x +y). When y is the 10s digit, the value is (10y +x). The difference of these is (10x +y) -(10y +x) = 9x -9y = 9(x -y).

The other problem is a "sum and differenc" problem. If the sum of two numbers (a, b) is s and their difference is d, the numbers can be found from ...
.. a +b = s
.. a -b = d
add these equations:
.. 2a = (s +d)
.. a = (s +d)/2 . . . . . . the larger number is the average of the sum and the difference
.. b = a -d = s -a = (s -d)/2 . . . . . you can find the other number several ways