Deepak remembers that the birthday is after 7^th May but before 10th May  , while Vishal remembers that birthday is after 8^th May  but before 12^th May . On which date of May is the birthday?

9

According to question , 

According to Deepak  birthday is after 7^th May but before 10th May

Possible date of birthday= 8 , 9      ------ ( 1 ) 

According to Vishal birthday is after 8^th May  but before 12^th May

Possible date of birthday = 9 , 10 , 11 , 12      ----- (2 ) 

from ( 1 ) & ( 2) 

Common satisfying date is 9 May

So birthday is on 9 May .