Yesterday was my birthday. For the first time in twenty years, the Roman numeral and the Hindu-Arabic numeral for my age are the same length. How old am I, and when will this happen again?
Edit: As noted correctly in the comments, I am now 40 (XL) and the next time will be when I am 51 (LI).
Glossographia 
Happy birthday! If I’ve correctly interpreted your puzzle, I believe it was an ‘extra-large’ one.
Indeed it was!
40 or XL and 60 or LX
Half right!
LV
Sorry, that’s still not correct.
A quick think suggests you are 40 (XC), 20 years ago you were 20 (XX) and this will happen again when you are 49 (IC).
Happy Birthday!
C is the Roman numeral for 100, not 50. Also, it is only permissible in ordinary Roman numerals to put I before V or X.
I meant L, rather than C, So IL isn’t used for 49. Hmmm….
I meant L, rather than C. You mean IL isn’t used for 49? Hmmm… Time to think a bit more slowly.
(Sorry for repeat comment, the first version went wrong).
IL is definitely not used for 49 in ordinary Roman numerals.
You are 40 (XL).
Next time will be 51 (LI).
That’s it! Congratulations!