Question : A pipe can fill a tank in 30 hours. Due to a leakage at the bottom, it is filled in 50 hours. How much time will the leakage take to empty the filled tank?
Option 1: 60 hours
Option 2: 85 hours
Option 3: 70 hours
Option 4: 75 hours
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Correct Answer: 75 hours
Solution :
The pipe fills the tank in 30 hours.
So, it fills $\frac{1}{30}$th of the tank in 1 hour.
With the leak, the pipe fills $\frac{1}{50}$th the tank in 1 hour.
The volume the leak empties in 1 hour $=\frac{1}{30} - \frac{1}{50} = \frac{5 - 3}{150} = \frac{2}{150} = \frac{1}{75}$
So, the leak will empty the full tank in 75 hours.
Hence, the correct answer is 75 hours.
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