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?

A.

3
2
a hours

B.

2
3
a hours

C.

4
3
a hours

D.

3
4
a hours

• Pipe A fills the tank in 'a' hours. Therefore, 1/a of the tank gets filled in an hour. On account of the leak, it takes 3a hours to fill the tank. Therefore, 1/3a 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
  therefore, x = 3a/2
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