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 then are opened together in the empty cistern, time taken to fill the cistern completely is ____.

• A. 20 minutes
• B. 15 minutes
• C. 10 minutes
• D. 5 minutes

Answer 1

The correct option is A 20 minutes

Inlet A can fill the cistern in 12 minutes
So, part of the cistern inlet A can fill in 1 min = $\frac{1}{12}$
Inlet B can fill the cistern in 15 minutes
So, part of the cistern inlet B can fill in 1 min = $\frac{1}{15}$
Outlet C can empty the cistern in 10 minutes
So, part of the cistern outlet C can empty in 1 min = $\frac{1}{10}$
Now, the part of the cistern that can be filled in 1 minute if inlet A and B and outlet C is opened together
$=\frac{1}{12}+\frac{1}{15}-\frac{1}{10}=\frac{5+4-6}{60}=\frac{3}{60}=\frac{1}{20}$

Now, the total time taken to fill the cistern completely
$=\frac{1}{\frac{1}{20}}=20\text{minutes}$