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 cistern completely?

Answer 1

Step: Find the total time required to fill the cistern completely

Given: Inlet A can fill the cistern in 12 hours. Inlet B can fill the cistern in 15 hours. Outlet pipe can empty the cistern in 10 hours.

Part of the cistern filled by inlet A in 1 hour $=\frac{1}{12}$
Part of the cistern filled by inlet B in 1 hour $=\frac{1}{15}$
Part of the cistern emptied by outlet pipe in 1 hour$=\frac{1}{10}$

So, part of the cistern filled in 1 hour when A, B, and C are opened together$=(\frac{1}{12}+\frac{1}{15})-\frac{1}{10}$
$=\frac{5+4}{60}-\frac{1}{10}$
$=\frac{9}{60}-\frac{1}{10}$
$=\frac{3}{60}$
$=\frac{1}{20}$
$\therefore$ The time required to fill the empty cistern completely when A, B, and C are opened together = 20 hours