Nitin remembers that his friend anniversary is after 9^th April  but before 12^nd April , while Ansh remembers that  his friend anniversary is before 15^th April but after 10^th April. On which date of  April is  his anniversary?

11

According to question , 

According to Nitin his friend anniversary is after 9^th April  but before 12^nd April 

Possible date of anniversary = 10 , 11   ------ ( 1 ) 

According to Ansh remembers that  his friend anniversary is before 15^th April but after 10^th April

Possible date of anniversary = 11 , 12 , 13 , 14      ----- (2 ) 

from ( 1 ) & ( 2) 

Common satisfying date is 11 April

So anniversary is on 11 April