Reverse Ages

Answer: Brian will be 25

Working it out by thinking about the numbers

 

If Brian's age begins with 1, his father's age should end with 1

Brian's father's age won't end with 1 until Brian is more than 20

If Brian's age begins with 2, his father's age should end with 2



Adding the same number of years to each age
 

So their ages will be each other's reverses in 11, 22, 33... years time.

Next time is in 11 years, 14 + 11 = 25


Using algebra to find numbers that are each other's reverses and are the correct distance apart
Brian's age written $ab$, Brian's age is $10a+b$
Father's age written $ba$, Father's age is $10b+a$.

$41-14 = 27$ so Brian's father is $27$ years older than Brian.

$$\begin{align}10a+b+27&=10b+a\\ 10a+27&=10b+a-b\\ 10a-a+27&=10b-b\\ 9a+27&=9b\\ a+3&=b\end{align}$$

$a$	$b$	Brian's age	Father's age
1	4	14	41
2	5	25	52
3	6	36	63
etc.