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 tiem will they take to fill the cistern completely?

Answer 1

Inlet A's 1 hour work to fill the cistern $=\frac{1}{12}$

Inlet B's 1 hour work to fill the cistern $=\frac{1}{15}$

Outlet's 1 hour work to emepty $=\frac{1}{10}$

Inlet's and outlet's together 1 hour work

$=\frac{1}{12}+\frac{1}{15}-\frac{1}{10}$

$=\frac{5+4-6}{60}=\frac{3}{60}=\frac{1}{20}$

$\therefore$ They can fill the cistern in 20 hours