A pump can fill a tank with water in 3 hours. Due to leakage in the bottom, it takes \(3\frac{1}{2}\)hours to fill it. In what time the leak will empty the fully filled tank?

Given:

Time taken by pump to fill the tank = 3 hours.

Time taken with leakage = 3 (1/2) hours = 7/2 hours.

Formula Used:

Net filling rate = Pump filling rate - Leakage rate

Time taken to empty the tank by the leak = 1 / Leakage rate

Calculation:

Pump filling rate = 1 tank / 3 hours = 1/3 tank/hour

Net filling rate with leak = 1 tank / (7/2) hours = 2/7 tank/hour

Let leakage rate be L tank/hour.

According to the formula:

Net filling rate = Pump filling rate - Leakage rate

⇒ 2/7 = 1/3 - L

Solving for L:

⇒ L = 1/3 - 2/7

⇒ L = (7 - 6) / 21

⇒ L = 1/21 tank/hour

Time taken to empty the tank by the leak = 1 / L

⇒ Time taken to empty the tank = 1 / (1/21)

⇒ Time taken to empty the tank = 21 hours

The correct answer is option 2.

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