Of course not. You need not answer that question:
1: You could ask “Why do you ask?” I have done that several times in my life after reading about that approach and it worked wonders. Most people then realize it’s an inappropriate question. Then I change the subject back to them.
2. You could just say you are uncomfortable with personal questions and change the subject back to the weather or ask how their family is doing etc.
3. My mother in law who was full of wisdom,used to tell myself and my SIL to IGNORE the question and change the subject. She said most people will not ask it again. I have used this approach and i it has worked every time for me.
You sound like you are a very kind person, but it’s not socially appropriate to ask personal questions and you have no obligation to answer ANY question. It took me until my 40’s though to realize that. and have “guts” enough to do the 3 above replies I note above. God bless~