In $1952$, I was as old as the number formed by last two digits of my birth year. When I mentioned this to my grandfather he surprised me by saying that the same applied to him also. The difference in our ages is ?
Now the way it has been solved is that let us assume that I was born in the year $19xy$ and my grandfather was born in the year $18pq$. Now as per the question :-
$19xy+xy=1952$ where $xy$ is my current age.
$\Rightarrow 1900 + xy + xy = 1952$
$\Rightarrow xy = 26$
$18pq+pq=1952$ where $pq$ is my grandfather's current age.
$\Rightarrow 1800 + pq + pq = 1952$
$\Rightarrow pq = 76$
Difference between the ages = $76 - 26 = 50.$
Now you all can see that this solution applied little logic with the assumption of my age and my grandfather's age. But what if the year given would have been $1989$ or $1999$ then we can't just assume that I would have been born in some $19xy$ and my grandfather would have been born in some $18xy$. It can very well happen that both of us would have been born in the same century.
I tried solving this by assuming that I was born in the year $abcd$ and my grandfather was born in the year $pqrs$ and following the same approach but it didn't helped me and then I turned to this solution that I have put up above.
So can anyone help me with this? Is it not possible to solve this problem by assuming years like I have or is it like we have to use some logic while assuming the birth years as the solution has done?
Thanks in advance !!!