Question

A pump can fill a cistern in 2 hours. Due to a leak in the tank it takes 2 (1/3) hours to fill it. The leak can empty the full tank in 

A. 7 hours 

B. 14 hours 

C. 8 hours 

D. 3 hours

Answer 1

A pipe can fill a cistern in: 2 hours 

Let a leak empty the cistern in: X hours

Due to the leak time taken to fill the cistern : \(2\frac{1}{3}=\frac{7}{3}\) hours

Part of the cistern filled by pipe in one hour: \(\frac{1}{2}\)

Part of the cistern emptied by leak in one hour: \(\frac{1}{x}\)

X = 14 hours

Therefore the leak will empty the cistern in 14 hours.