# A tap fills the tank with water in 2 hours. But due to the leakage of water due to a leakage in the tank, the tank fills in $2 \frac{1}{3}$ hours. I

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A tap fills the tank with water in 2 hours. But due to the leakage of water due to a leakage in the tank, the tank fills in $2 \frac{1}{3}$ hours. In how many hours will the leakage empty the tank?
1. $2 \frac{1}{3}$ hours
2. 7 hours
3. 8 hours
4. 14 hours

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Correct Answer - Option 4 : 14 hours

Given:

Time taken by a tap fills the tank with water = 2 hours

Time taken by a leakage = 2,1/3

Formula used:

Efficiency = Work/Time

Calculation:

Part of the tank filled by the pump in 1 hour = 1/2

Total part of the tank filled by the pump and leak in 1 hour = 1/(7/3)  = 3/7

so part of the tank emptied by the leak in 1 hour = 1/2 - 3/7

⇒ (7 - 6)/14 = 1/14

∴ The leak will empty the tank in 14 hours