A pipe can fill a cistern in 10 hours. Due to a leak in the bottom it

1.	A pipe can fill a cistern in 10 hours. Due to a leak in the bottom it is filled in 12 hours. When the cistern is full, in how much time will it be emptied by the leak?
Answer» Given, A pipe can fill a cistern in = 10 hours Due to leakage it get filled in = 12 hours ∵ Without leakage work done by pipe in 1 hour \(=\frac{1}{10}\)part ∵ With leakage work done by pipe in 1 hour \(=\frac{1}{12}\)part ∴ Work done by leakage in 1 hour =\(\frac{1}{10}-\frac{1}{12}=\frac{12-10}{120}=\frac{2}{120}=\frac{1}{60}\)part Hence, the cistern will be emptied by leakage in \(=\frac{1}{\frac{1}{60}}\)=60 hours.

A pipe can fill a cistern in 10 hours. Due to a leak in the bottom it is filled in 12 hours. When the cistern is full, in how much time will it be emptied by the leak?

Answer»

Given,

A pipe can fill a cistern in = 10 hours

Due to leakage it get filled in = 12 hours

∵ Without leakage work done by pipe in 1 hour \(=\frac{1}{10}\)part

∵ With leakage work done by pipe in 1 hour \(=\frac{1}{12}\)part

∴ Work done by leakage in 1 hour =\(\frac{1}{10}-\frac{1}{12}=\frac{12-10}{120}=\frac{2}{120}=\frac{1}{60}\)part

Hence, the cistern will be emptied by leakage in \(=\frac{1}{\frac{1}{60}}\)=60 hours.