 # A cistern has two inlets A and B which can fill it in 12 minutes and 15 minutes respectively.

Question:

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

Solution:

Inlet A can fill the cistern in 12 minutes.

Inlet B can fill the cistern in 15 minutes.

Outlet $\mathrm{C}$ empties the filled cistern in 10 minutes.

Part of the cistern filled by inlet A in one minute $=\frac{1}{12}$

Part of the cistern filled by inlet B in one minute $=\frac{1}{15}$

Part of the cistern emptied by outlet $\mathrm{C}$ in one minute $=-\frac{1}{10}$ (water flows out from $\mathrm{C}$ and empties the cistern)

Part of the cistern filled in one minute with A, B and C working together $=\frac{1}{12}+\frac{1}{15}-\frac{1}{10}=\frac{5+4-6}{60}=\frac{3}{60}=\frac{1}{20}$

The time required to fill the cistern with all inlets, $A, \mathrm{~B}$ and $\mathrm{C}$, open is 20 minutes.