Prakash remembers that his wife Roshni's birthday falls after $$20^{th}$$ May but before $$28^{th}$$ May, while Jyoti remembers that her mother Roshni's birthday falls after $$26^{th}$$ May but before $$30^{th}$$ May. On what date does Roshni's birthday fall ?

As per Prakash, Roshni's birthday falls after 20 May but before $28 May. Thus, the number of possible dates is 21 May, 22 May, 23 May, 24 May, 25 May, 26 May, 27 May.

As per Jyoti, Roshni's birthday falls after 26 May but before 30 May. Thus, the number of possible dates is 27 May, 28 May, 29 May.

Thus, we can see that only May 27 is the common date in both cases. 

Roshni's birthday is on $$27^{th}$$ May.