The upside is that it is illegal for somebody to ask for your age at work. Unfortunately, individuals ask the question all the time anyway. Bearing that in mind, you ought to give some consideration as to how you’ll answer the question when you are caught by surprise. If your colleagues notice that you look like dear ahead of headlights, you will solidify their impression that you are not fit to handle the top job that awaits.
If you are not inclined to divulge your age and also don’t want to come off rude about it, playfully smile and say that you’re old enough for the job. But if you find no qualms about sharing, go on ahead! Regardless of how you opt to deal with the entire situation, prepare to answer the question with confidence, and just move on. The whole underlying reason for it all is to prevent it from becoming a topic for continued discussion and speculation. To put yourself in a better position to control the narrative, have a response already thought out before the question being asked.