Pipe A fills the cistern in half an hour and pipe B in 40 minutes, but owing to a crack in the bottom of the cistern it is found that pipe A now takes, 40 minutes to fill the cistern. How long will B take now to fill it and how long will the crack take to empty it?

The leak empties in 1 hour and B fills in 2 hours
B fills in an hour and the leak empties in 2 hours
B fills in an hour and the leak empties in an hour
Data inadequate

Correct Answer: B fills in an hour and the leak empties in 2 hours

Explanation:

Let the leak empties it in T hours
From the given rule, we have (T x 30) / (T - 30) = 40
∴ T = 120 minutes = 2 hours.
Now, from the question, applying the rule, we have time taken by B to fill the tank when crack in the bottom develops
= (120 x 40) / (120 - 40) = 60 minutes = 1 hour

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