let A be area of vessel.
a be area of hole
at any time let H be level of water in the vessel.
Time taken for water level to get reduced from H to 0 is given by
Time taken for water level to get reduced from H/2 to 0 is given by 
therefore Time taken for water level to get reduced from H to H/2 is given by (T1)=
---
---------------------1
and Time taken for water level to get reduced from H/2 to 0 is given by (T2) =
-------------2
on dividing eqn 1 by 2 we get. T1/T2 =