- Pipe A can fill a tank in 'a' hours. On account of a leak at the bottom
of the tank it takes thrice as long to fill the tank. How long will the leak
at the bottom of the tank take to empty a full tank, when pipe A is kept
closed?
(1) (3/2)a hours (2) (2/3)a (3) (4/3)a (4) (3/4)a
Solution:
Pipe A fills the tank in 'a' hours. Therefore,
of the tank gets filled in an hour. On account of the leak it takes 3a hours to
fill the tank. Therefore,
of the tank gets filled in an hour. Let the leak at the bottom of the tank take
'x' hours to empty the tank. Hence,
1/x
of the tank gets emptied every hour.
1/a - 1/x =1/3a => 1/x =1/a - 1/3a = 2/3a
Hence, x =
3a/2
