Question

A cistern has two inlets A and B which can fill it in 12 hours and 15 hours respectively. An outlet can empty the full cistern in 10 hours. If all the three pipes are opened together in the empty cistern, how much time will they take to fill the cistern completely?

Answer 1

Given,

 Inlet A can fill the cistern in = 12 hours

 Inlet B can fill it in = 15 hours

 Outlet pipe can empty it in = 10 hours

 ∵ Work done by pipe A in 1 hour \(=\frac{1}{12}\)

∵ Work done by pipe B in 1 hour =\(\frac{1}{15}\)

 ∵ work done by outlet pipe in 1 hour \(=\frac{1}{10}\)

∴ Net work done by 3 pipe in 1 hour \(=[{\frac{1}{12}+\frac{1}{15}}]-\frac{1}{10}=\frac{9}{60}-\frac{1}{10}=\frac{9-6}{60}=\frac{3}{60}=\frac{1}{20}\)part

Hence, time taken by 3 pipes to fill the tank \(=\frac{1}{\frac{1}{20}}\)= 20 hours