IPMAT Rohtak 2019 (QA) - Two pipes P and Q can fill a tank in 20 hrs and 25 hrs respectively while a third pipe R can empty the tank in 30 hrs. If all the pipes are opened together for 10 hrs and then pipe R is closed, then in what time the tank can be filled? | PYQs + Solutions

IPMAT Rohtak 2019

Arithmetic

Time & Work

Medium

Two pipes P and Q can fill a tank in $20$ hrs and $25$ hrs respectively while a third pipe R can empty the tank in $30$ hrs. If all the pipes are opened together for $10$ hrs and then pipe R is closed, then in what time the tank can be filled?

\frac{400}{23}

hrs

\frac{400}{27}

hrs

\frac{200}{23}

hrs

\frac{200}{27}

hrs

Correct Option: 2

Work they all do in one hour:

\frac{1}{P}=\frac{1}{20}

\frac{1}{Q}=\frac{1}{25}

\frac{1}{R}=-\frac{1}{30}

When they are all opened for 10 hours:

10[\frac{1}{20}+\frac{1}{25}-\frac{1}{30}]

10[\frac{15+12-10}{300}]=\frac{170}{300}

Now pipe R is closed, we need to find in how much time P and Q will fill the tank now

Remaining capacity of the tank

=1-\frac{170}{300}=\frac{130}{300}

Let remaining time be

x

, then:

x[\frac{1}{20}+\frac{1}{25}]=\frac{130}{300}

x[\frac{9}{100}]=\frac{130}{300}

x=\frac{130\times100}{300\times9}=\frac{130}{27}

So, total time

=10+\frac{130}{27}=\frac{270+130}{27}=\frac{400}{27}

hours