Question : A pump can fill a tank with water in 3 hours. Because of a leak, it took $3\frac{1}{3}$ hours to fill the tank. In how many hours can the leak alone drain all the water in the tank when it is full?
Option 1: 21
Option 2: 15
Option 3: 30
Option 4: 10
Correct Answer: 30
Solution :
Time taken by a pump to fill a tank = 3 hours
Part of the tank filled by the pump in an hour = $\frac{1}{3}$
Let the time taken by the leakage to empty the tank be $x$ hours.
Part of tank emptied by the leakage in an hour = $\frac{1}{x}$
Time taken by the pump along with the leakage to fill the tank = $3\frac{1}{3} = \frac{10}{3}$ hours
Part of the tank filled by pump along with the leakage in an hour = $\frac{3}{10}$
According to the question,
$\frac{1}{3} - \frac{1}{x} = \frac{3}{10}$
$⇒\frac{1}{x} = \frac{1}{3} - \frac{3}{10} = \frac{10-9}{30} = \frac{1}{30}$
$\therefore x = 30$ hours
Hence, the correct answer is 30.
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